I have always understood it as a double irony, intentionally written so to make that very point, Tunesmith. It's a rare writing trick, but great when you can pull it off; Carly does so in spades in this song.

The only other example of such exquisite irony I can think of is the 10CC hit of the mid-1970s: "I'm not in love" - when he clearly is. But there are a few others around, I just con't think of them rioght now.