Is there more to this in the book that the movie doesn't cover?
There is no book.
The scenes set after the original Godfather are entirely original and not based on any novel although Puzo co-wrote the movie's screenplay with Coppola.
Fredo has always been a weak person and something of a bungler. He's never really been trusted with anything other than errards or "showing the guests a good time"....he's the "party organiser".
He's a terrible liar and can't keep lies straight in his head.
It's not clear whether Fredo's admission that Johnny Ola showed him the nightclub was intended/meant to be overheard by anyone (especially Michael) since the comment was directed to Sen. Geary but its indicative of Fredo's character than he makes this mistake.
Plus...he's drunk...as the script makes clear
Our group are in a large Havana bar; the walls totally covered with hundreds of fifths of different types of rum and other liquor.
A couple of the girls from the show are out with the men; Yolanda herself is giving them a private song and dance.
Fredo is a little loaded, and especially attentive to Michael this night.
Fredo's party standing on the ramp, looking down at the
spectacle. They're a little woozy from the drinks and late
hour. Michael is with them, but now we sense he is using
this time, with them all exhausted and drunk, to come to some