I don't know if ONLY the user that started the thread (plus the admins) should be allowed to close a thread but it would make sense for me to allow him to say that he got the answer he was looking for. Anybody that was not satisfied that the issue was actually "closed" could start a new thread.

I haven't seen many closed threads (in fact I don't remember seeing any)... It would be really helpful if they were marked as closed on all searches (not just a tag) but we have already another thread for this.