As a side note this is reason I've always believed building an business/app of any importance on-top of another site is just crazy. You're at their mercy and there's nothing you can ever do to stop them shutting you out.
And almost any business will be dependant, to some extent, on others. It's a question of how many of your dependencies are irreplaceable, and how likely they are to shut you out.
See for example http://en.gentoo-wiki.com/outage-10-08.html - they went down and lost all their data because the hosting company had a fight with the people who owned the building where the servers were kept. (Including backups, which made the host irreplaceable - with offsite backups, that wouldn't have been the case.)
Building on a site like twitter might increase the risk of being cut off on a whim, but it probably decreases the risk of competitors.