There is no verb "to pileate", but if there were, I would imagine it would mean something like "to act pointy-headed, or to make an assertion in the manner of a pointy-headed person."

"We don't have to explain our actions if they aren't logical," he pileated.

Or, "It's not plagiarism if I change more than one-third of the substantive nouns in the original," he pileated.

A