And the idea that a tune should have the same time signature all the way through doesn't work when you're dealing with music in many traditions.

It's the kind of misunderstanding that used to involve collectors adjusting the tunes to impose a single time signature, and assuming the people they were collecting from were just making mistakes.

Nowadays it isn't the collectors that do that, but we do it a lot of the time, because we've developed cloth ears from listening to too much canned music.