Zorba was the same in his columns. He would slip “ironically” in to most columns. Usually it was referring to an interesting point rather than irony. For example, “that was the sea eagles’ biggest win against the Steelers at brookvale. Ironically manly hasn’t won in Wollongong for 3 years.”
And he was a trained journo.
As for Alanis, the only way rain on your wedding day could be ironic is if she was marrying a weatherman, and he predicted a fine day.