that may be the law but in 8 years here, I’ve never been asked by the police to show my passport. Just my DL. But if one is only a tourist, without a DL, then yes, they would need to show it.
As it’s been said many times, the requirements depend on the office. I moved the required funds to Thailand and applied to change my tourist visa to Non-O for retirement at the Chiang Mai office merely days later. The application was accepted and I was told to go back at the end of the month to get the stamp.