Originally Posted by
rnavuc
I'm just not comfortable giving them my account info.
Trust that instinct.
Originally Posted by
rnavuc
[...] there is no way to prove it from BA's perspective. They have the transfer system in place for a reason
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.