Jack E. Leonard..... Wikipedia says he was a nice and kind guy in private w his friends. Maybe he would stay in character and use people like your friend to get revved up for his nightclub act. Then Frank was in on the “joke” and would tip the person that got dumped on
It’s possible.
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...