Update: As of api-v2.2, it's also possible to write questions and answers via the API.
There are at least a few examples in use, of API 2.1 apps, that write comments. See:
- The Quick Media Solutions appThe Quick Media Solutions app
- The StackX Android appThe StackX Android app
- The SX.el Emacs appThe SX.el Emacs app
Re:
Am I correct in thinking that only comments can be written and not questions?
Yes, that's correct. Except for the super-secret, official, Android app that's under development. It presumably uses an API that's not publicly documented.