Tautosemy?

While listening to talk show radio, especially during interviews, I sometimes hear callers saying "I'll take the answer on/off the air". In both cases it means that they are willing to hang up immediately after asking the question without engaging in a discussion, presumably to save some time and to allow more people to call in.

I could not decide which of "on" or "off" is the "right" one:

I'll take the answer on the air means "as opposed to on the phone" (the technicalities of the live radio show require callers to silence the radio while their call is live to avoid interference), and I'll take the answer off the air means "when my call isn't on the air anymore".

For a word that may have opposite meanings there is a term "enantiosemy"; should the opposite phenomenon (antonyms being used interchangeably) be called "tautosemy"?