Off course it is possible to read and write a code from an RFID-Chip or Card.
On simple chips, it is nothing more then a code or a number, which identifies it uniquely.
But there are several techniques, which prevent you from doing that. Take an access-key:
It has several frequences with different codes, which cannot be read with a simple reader. Some are hardware protected and cannot be changed. There are variables stored on to it, which change on every entrance. More or less like your car does it, too.
So, all in all: Could be possible on a canteen chip, but must not be. Nearly impossible with an entrance chip!
That someone "sometimes" lost his canteen-chip... Come on! Who should believe that

And helping anyone to bypass a terror protection?