The local exchange that I use because of their excellent rates has never asked me for my passport even when I exchanged 65,000 baht last week. They just ask for a local phone number which I wrote on a piece of paper for them. It could be any number because they never check.
SuperRich on the other hand always took a photocopy of my passport before the transaction. My local exchange has slightly better rates than SuperRich and being local I walk there and don't have to catch the MRT to make a transaction.