What you're saying makes sense, but I think the difference is more subtle than that.

And I don't think you're thinking of the right lines of the song when you're defending it. For instance, "It's the good advice that you just didn't take." That doesn't fit any of your definitions.

I think they were discussing the song on one of those many VH1 "Celebreties Reminisce" shows. Someone made a funny point that if we were to believe that Alanis were a very creative songwriter, she could have put lines in her song that weren't ironic on purpose, thus writing a song about irony that contained phrases which weren't ironic, thereby being ironic in itself