If my salary depended on the Twitter API right now I'd be scared shitless.
A better strategy is to trust somebody (/an API) until they give you good reasons not to. Admittedly, twitter seems to have broken that trust. I personally would't use them as a platform, unless the benefits clearly outweigh the risks of them haphazardly cutting me off.
The challenge is to determine, in advance, if the platform you are writing for will maintain some reasonable level of access to the API, both now, and in the future.
This is evidence for an unfortunate confusion about the usage of the term "API". There is a world of difference between a third-party library and a third-party service, each of which can be said to have an API. There are plenty of pieces of software which rely on one kind of API but not the other.
It is entirely possible to write software that doesn't rely on a third-party service. If that's the point you're trying to make then great! You see the thing is about relying on third-party services is that a great amount of trust must exist between the application and the service. It's a good way to go, but when there's no actual money moving between the app and the service, everyone has reason to be a little concerned.
The question you have to ask yourself is how much leverage the third-party has over you if they decided they want to screw you over. Even still, you may want to write for that platform if the $$$ is there. Look at iOS platform - Apple totally owns you. Or, even better, look at the PS3/Wii/XBox platforms - the owners of those APIs have even more control over what you can do - but still very profitable platforms to develop for.
At the end of the day, a judgement call has to be made. No easy rules.