As a descriptive, not prescriptive, grammarian, the deeper meaning that Morissette's song accidentally has is that there were at least three or four distinct extant definitions of "irony", many people were very sure their definition was universal, and none of those people were right.

It's sort of shocking this five-letter word turned out to have several simultaneous different non-overlapping meanings, with so many people not even realizing the differences in the way other people were using the word. There's probably a PhD thesis in there somewhere. No joke, irony, or sarcasm.