The same type of thing happened to me, way back when, only no detention and it didn't get ugly. But the teachers mistake was stoopidly obvious. She kept referring to Henry "Wordsworth" Longfellow. I, of course, couldn't STFU, and corrected her every time. "Don't you mean "Wadsworth"?" She, then, kept passing it off as a tomayto/tomahto type of thing(I hope my phonetic explanation worked). I told her that my Mom and Henry shared the same home town, and NOBODY said it that way.
The other kicker to the story? This happened at "Longfellow Intermediate School"!