John Borthwick, who funded bit.ly via his Betaworks investment group, explains the details of his offer here, along with a bit of pro forma condolence for the demise of his competitor: “Sad day yesterday to see tr.im announce that they are shutting their doors, after failing to make a business of a nice service with a great URL.”

To me, that sounds a bit like a mafia don shaking his head a tad wistfully after hearing that one his old rivals got bumped off, then sending a big bouquet to the funeral. And I think that the tr.im team, as well as some of bit.ly’s other competitors, may take it in the same vein.

UPDATE: I spoke to Eric Woodward, CEO of Tr.im’s parent company Nambu Networks. As I thought, he’s uninterested in working with Bit.ly, either directly or via 301works, the third party archive Borthwick has proposed. His response: “Why would I want to upload all my of data to Bit.ly?” When I suggested that this might be a good move for his users, he allowed that it still might happen — if he can’t find a buyer for Tr.im. And that’s a distinct possiblity: Woodward said he has been looking for a buyer for the past few months, without success.

But Borthwick’s proposal also sounds like a good one to me. I’ll let the wiser Webheads explain whether it’s a real solution for the problem that tr.im’s failure will create for the Web, namely, the notion that lots of Web addresses, shortened for use in social Web services like Facebook and Twitter, will stop working one day.

And if you do think it’s a real problem and not just an annoyance for the service’s users, as well as for Web sites that got referral traffic from the service, then someone’s going to need to think of something. We’re going to see more of this.

That’s because if there is any business at all in URL-shortening, it’s going to be a scale business that ends up in the hands of a couple competitors, max. Just like search. And that means that dozens of mom-and-pop competitors (here’s a visual snapshot, taken last fall, of 117 URL-shorteners) are going to fall by the wayside.

Right now Bit.ly looks to be the Google (GOOG) of URL-shortening, and there is some griping that it got that status unfairly, via a deal with Twitter that made it the service’s default shortener last May (type a long Web address into the message box on Twitter’s Web page, and the service will automatically convert it into a bit.ly link–like this). Not true, says Borthwick–the Twitter deal helped, but it’s not responsible for the majority of Bit.ly’s traffic.

But there’s no reason for Borthwick, Bit.ly or Twitter to be defensive about the deal. If Twitter wants to pick a preferred vendor/partner/developer for any or all of its services, it should do so. It’s not going to do that very often; one of the main reasons that Twitter has taken off is the ecosystem of developers who have built innovative stuff using the service’s open architecture, and it won’t want to discourage that.

And if Twitter wants to work with someone it’s already doing business with–prior to Twitter’s most recent funding round, Betaworks owned a sizable slug of Twitter’s stock, via Twitter’s acquisition of Betaworks portfolio company Summize a year ago–there’s no problem with that, either.

In any case, the Bit.ly/Betaworks guys have other things to worry about. They still need to figure out how to take the data stream they’re mining from all those tiny Web addresses they’re making and do something useful/valuable with it.

Then again, so does Twitter.

ComScore says Twitter logged 30.1 million search queries in May, more than Time Warner Cable (TWC), but not even on the same playing field as search also-rans like Ask.com.

But what if comScore is dramatically undercounting Twitter’s search–not just the standard undercounting that Web publishers always complain about, but something more significant?

It’s a given that comScore is undercounting. I know this because the research outfit told me so: The company confirmed today that it only measures searches executed at Twitter.com. But at least half of Twitter’s users are accessing the service without visiting the site, via third-party clients like Tweetdeck. And within that group of users is the power-user set, which is far more likely to be executing searches, many times a day in some cases, than Oprah fans who just joined the service last month.

So it’s easy enough to conclude that the majority of Twitter’s searches are going uncounted by comScore (SCOR). But how big is the gap? I’ve asked Twitter to share its search numbers, but I’m not holding my breath on that one. (UPDATE: See bottom of post)

In the meantime, let’s do some guesstimating.

Start with this year-old post by John Borthwick of Betaworks, who at the time was an investor in Summize, a Twitter search engine at the time (Twitter later bought Summize outright).

Borthwick reports seeing a huge number of search queries on Twitter on the opening day of Apple’s (AAPL) 2008 developer conference, topping out at an average of 190 queries per second. Tease that out over a full day, and you get 16.4 million searches in 24 hours.

For argument’s sake, let’s say that most of those searches occurred in an eight-hour stretch before, during and after Steve Jobs’s pronouncements that day, and knock that total down by two-thirds, to something like 5.5 million queries.

Steve Jobs pronouncements are rare things so it would be wrong to assume that Twitter sees similar usage patterns every day. But then again, Twitter has had an insane growth spurt in the last year: The most recent comScore traffic numbers peg monthly visitors at 32 million world-wide, up from a couple million a year ago.

See where this is going? Again, for argument’s sake, let’s say that Twitter’s peak traffic a year ago is now close to daily traffic today, and extrapolate that 5.5 million query guesstimate out for a month: You get something closer to 165 million queries.

Want to tweak any of my assumptions above? Be my guest. But no matter how you cut it, I’m sure that Twitter’s real search numbers are going to be several times higher than comScore’s number, at the very least.

Again, this matters in the end because Twitter’s most compelling investment thesis is that it can provide real-time search. And for that to mean something, the company is going to have to start registering as an actual search competitor at some point, not just to Time Warner Cable but to Yahoo (YHOO), Microsoft (MSFT) or even Google (GOOG). So how close, or far away, is that from happening?

UPDATE: Twitter cofounder Biz Stone responds, but declines to hand out any numbers. No surprise. I am a bit surprised to see him play down the importance of search at Twitter. I wonder if his investors are also surprised.

We don’t share absolute data such as total requests or queries per day but we do look at the whole ecosystem when we measure these things (not just Twitter.com).

Also, we are focused on the sharing and discovery of tweets so comparing Twitter to web search is interesting but not necessarily how we would measure success.

The story: Big pharma Johnson & Johnson (JNJ) has rolled out a Web clip (below) in which a snarky, knowing commentator gripes about the social pressure to “wear” babies in slings, carriers, etc–and the Motrin-ready aches that “wearing” a baby can cause. And in the last few days lots of blogger/Twitterers have agreed that:

• The ad is offensive.
• Motrin/JNJ doesn’t “get” social marketing.
• Something should be done! Maybe a boycott.

How many bloggers/Twitterers are actually complaining about this? And are there enough to hurt JNJ, which made an estimated $1 billion in profit from Motrin each year? Mmmmmmaybe.

Tools like Google’s blog search and Twitter’s Summize search will tell you that, yes, some number of people are chattering about this on the Web. And as of 8:07 a.m. Monday, the Motrin.com site was down, whatever that means. But from what I can tell, only a few thousand people have actually seen the ad on Google’s (GOOG) YouTube. I’ve asked video watcher TubeMogul for info on the ad’s audience and will update when I get it.

But even if the outrage is widespread, it’s going to be hard make a connection between online chatter and real-world results. Otherwise Ron Paul would be the 44th President of the United States.

Meanwhile, at the risk of a cyber-stoning, let me say that I don’t think the ad–which seems to be aiming at the same set of people who buy very expensive strollers but feel a bit conflicted about doing so–is an outrage. And neither does the person who does most of the baby-wearing in my house.

I ran it by her in the twilight hours this morning, between feedings, and she shrugged: “It’s true.” Then she went back to sleep.

UPDATE: Twitter Moms unite! JNJ has apologized, and is very, very sorry. Kathy Widmer sends Forbes.com this mea culpa:

I am the Vice President of Marketing for McNeil Consumer Healthcare. I have responsibility for the Motrin Brand, and am responding to concerns about recent advertising on our website. I am, myself, a mom of 3 daughters. We certainly did not mean to offend moms through our advertising. Instead, we had intended to demonstrate genuine sympathy and appreciation for all that parents do for their babies. We believe deeply that moms know best and we sincerely apologize for disappointing you. Please know that we take your feedback seriously and will take swift action with regard to this ad. We are in process of removing it from our website. It will take longer, unfortunately, for it to be removed from magazine print as it is currently on newstands and in distribution.”

Lesson: Carping on Twitter does indeed work. Sometimes.