No, irony does not depend on correctness. When the discussion is X, if your only input is -X, then it's ironic in the face of a discussion on shooting down ideas.
It would be ironic for me to make a typo while bashing your spelling prowess. It would not be ironic if I didn’t.
It is similarly ironic that the Alanis Morrisette song about irony mostly mentions non-ironic things; “rain on your wedding day” isn’t ironic! And that’s ironic!
Or are you ironically shooting down my idea that it is a skill?