The more I think about your theory, the more I consider a possibility. But it implies an elaborate hoax on the part of two people. And for what purpose? I could see doing such a hoax in public where there would be some reaction, then tipping the target as a way of making amends. And doing it against a private person would be considered distasteful by many. It smacks of ganging up on someone with less advantage than you. And, this wasn’t a public thing. No one would know but them. If true, my buddy was sure scammed.
The other thing is, it will forever remain a theory. We can’t prove a negative. There’s no way it could be proven to be true, unless the Sinatra family would be open about such tricks. I rather doubt that...
Jack E. Leonard and Frank are getting bored on the road so they have a running joke which your friend is the victim of....But $100 was a lot back then so the feel your friend got ample compensation
You have already shown that at least half of a joke was going on just by Frank tipping him the $100. And of course Jack E. Leonard will find out about this. So it becomes an ongoing joke between the two plus their entourage (my theory)