You're right. The "malapropism" part I hypothesized was "stretching" things. (Though I actually admitted that in that same post.)
But the point remains that a song entitled "Ironic" is perfectly ironically named if it carries zero lyrical irony. In that situation, "ironic" is apropos, then. Or, to reiterate this point in a third way, it is a good title (even the song itself is below average).
Maybe Alanis landed on that by mistake, who knows, but anyone who claims that the song is dumbly titled because they think the title is not ironic is not only flatly wrong but is either ignorant of or cognitively dissonant to the definition of irony. Well, I guess there's at least one more option: the person might also not recognize that a song with ironic lyrics with the title "Ironic" isn't so much ironic as it is "About Irony."