That's a fair point, but "The Real Book" was always referred to as a 'fake book' by every Jazz musician I ever met, though. I honestly don't think licensing has anything to do with the term.

For decades a legal version was available called "The New Real Book", but "The Real Book" was the name of the original*, unauthorized fakebook - preferred by every jazz musician I met - until the latest edition when the rights were finally secured by a major publishing house with edition 6.

*I used the term 'original', but to my knowledge fakebooks were around since the 20's or before. "The Real Book" was already a play on that back in the 70's. And typically none of them were authorized.

EDIT: Sorry for haphazardly continuing to update this but I was trying to dig up more. Here's the link I was trying to find[0] With previous discussion here on HN[1]. It states, 'They called them “fake books” because they helped musicians fake their way through unfamiliar songs.' However, it's certainly not the only possible explanation.

[0] https://99percentinvisible.org/episode/the-real-book/

[1] https://news.ycombinator.com/item?id=26737142