What would Carly Simon say?

So I've heard yet again on the radio, Carly Simon's 'Your So Vain'. The repeated chorus is:

You're so vain, you probably think this song is about you

You're so vain, I'll bet you think this song is about you

Don't you? Don't You?

Now I don't know much about this song, who it's about, how angry she was etc, etc, but the lyrics are begging the man to dare to think she cares enough to actually write this song about him....but, well, the unfortunate mistake Carly made was that, yes, the song WAS about him. If not, who else is it about?