I do not know about SIR, but I have surely purchased firearms over the phone/Internet and only provided my PAL NUMBER, not a copy.
But when it comes time for a transfer, a licenced dealer still needs to know full name, address, DOB, etc for the buyer. In a gun deal from a private individual, the buyer must contact CFC with a number of personal details that are not on the PAL.
I think the likelihood of a photocopied PAL being used to purchase a gun is just about zero.
(After all, most criminals buy unregistered guns from fellow criminals, and avoid all of the hassle and BS.)
Doug