It's not an assumption, normally people DON'T keep track of any of this. When I go to the bar and buy a beer with $10, the bar tender is for sure NOT writing down the serial number on the bill, checking my ID, and forwarding that information off to the FBI. The $10 can sit for a day or two in the till, and then be returned to another customer as change. In this way it continues its anonymous passage through the economy.