Trust that instinct.
The broker would not "transfer" your Avios. They would log in to your account, as you, and redeem your Avios for a ticket in the name of one of their customers. That person would pay them for the ticket. Your BAEC account would remain associated with the ticket.
Indeed, and if the person who buys the ticket from the broker has done it before and is already on BA’s radar, that’s an immediate red flag.
One can claim one was just booking for a friend or colleague but if that person’s got previous, one’s case starts to look very weak.