Yeah surprisingly seems to be true. I've bought a SIM with cash before. They do ask for your full name and address at the very least but its conceivably possible to do with a fake name and address and topping it up with cash every so often.

But almost nobody does that, and it doesn't really change the point of the OP since if you ever use the sim for identifiable comms or in identifiable locations or sign into other services in your name using it.