Why would they have to buy one? It's an incredibly simple thing to create. It would take more work to buy one and integrate it into their system/API than just create it from scratch.
All snark aside, putting together something as rich as bit.ly is NOT an incredibly simple thing to create. And twitter will need to incorporate such functionality in there, or people WILL find ways to use their favourites to get the functionality they're used to.
The way they have done the default has always bugged me--they don't shorten URLs as you type them so if you're over 140 characters it won't shorten, but if your message is under 140 characters it sometimes (only sometimes) shortens the URL. Which is unnecessary and annoying, if the space is there why not show the full URL?
Making a functional link redirector? Yes, absolutely. There are frameworks that you could toss something together with in an hour that would scale enough for most people's purposes. With some frameworks you can get pretty close to true internet-scale scalability in a weekend. (I'd think Yaws and Erlang here.) I've seen framework tutorials use this as the demo, and, again, we're talking things that can get awfully close to internet scale without much work.
Making all the stuff that apparently surround link redirectors in some desperate attempt to make it "monetizable"? It would take longer, but unlike the case for "replicating Stack Overflow" where all the extra stuff is the real value and will take more than a weekend, that's all extra stuff that nobody really cares about very much in this case. A page that takes a URL, returns a URL, and does nothing else really is enough for the vast majority of uses.
It's a different class of problem. This truly is a fundamentally trivial problem. I personally see no reasonable way to "monetize" this trivial service, because the market value of a URL synonym is going to trend very strongly towards zero due to effectively infinite supply.
(Much as your point was that it's hard to recreate bit.ly rather than the weekend snark, note my point is more that doing that is a waste of time, mostly-crap features done to benefit the redirector, not the user, and that this truly is easy to recreate enough to drive supply sky-high.)