Do you really think your broker would be hurt by revealing their name? It says something unfavorably about your ego to think anybody cares.
Possibly when your order sits on the bid on one exchange, someone lowers his ask to take all bids except your bid, thus create a cross order, his ask is equal to your bid but on another exchange, then your exchange fires your order to lift the ask on the other exchange. Check if the filled exchange is same as the exchange you send.
This is a good answer The rep you spoke to should have known the answer, if I correctly assume this a common question. Markets move so fast that switching back and forth even back to the original exchange could change whether you provided liquidity. Let it go if it is not an ongoing issue.
I do not understand what I am reading here. So with stocks you can get money for your orders sitting on the line and not getting filled? What kind of racket is that?
Why would you get money for having an order on the book? Why would you get "extra" if your order is filled? I do not trade stocks, and so am not privy to this stuff.