What happens at one book, doesn't carry over to another book. Most people don't even know books that have the same provider. Unless the player was notified that he is banned at all Betby books, pay him. The player made two live tennis bets. There is no abuse. He didn't know he was banned at Duckdice. A lot of times a point can be made for both sides. Here there is no reason for the player not to be paid.
May I know if you have an evidence to back up this claim? That things does not carry over? because far as I know, it does carry on to another casino [in your word: book] if they share the same provider, there are instances of it.
I've had talk with several casinos' representative and they confirm this. It's also been made known publicly by several representative throughout the boards of this forum that they communicate with their "competitor" to keep gambling environment safe from abusers.