They do, but that doesn't slam the door shut on a developer/business purely for the sake of slamming the door shut on a developer/business.
From what I've seen, Facebook encourages API usage. Twitter encourages it until you make money, then they shut you down - often stating they're building a similar app/service and you'd be competing with them -- only then to never launch said app/service.
Twitter as a platform isn't worth much (as evidenced by year after year of not turning profits). The value in Twitter is the data - but they are locking it away.
Why not go the Google route and charge for API usage over a certain threshold. Twitter could stop caring what users do with the data, and make money as their ecosystem grows and becomes more successful.
I think this is what makes people so hostile towards Twitter.
Twitter neither clones successful services nor continues to run those they acquire. Instead they either shut them down, or acquire then shut them down - meanwhile completely missing opportunity after opportunity to capitalize on their massive ocean of data.
It seems, based on history, Twitter is not interested in running many services around the Twitter platform/API/data. Instead they really just want to be "Twitter".
I say, let them do what they do best - acquire data and build great API's. Let 3rd parties build Twitter's userbase and data, but charge them for access to the API. It's a simple monetization plan.
Happens all the time. App.net was original an "app store" for facebook but they decided to make a competitor called App Center or something and told App.net they could either be acquired or shut down.