Aye, when you isolate the FBH from the receiver by pulling the fuse or unplugging it, then plug it back in, the receiver searches for a signal over a particular frequency range...when you press the off button on the remote fob during the pairing process, the receiver on the car picks up the signal and recognises it, pairing it to the new fob's frequency.
The frequency might only vary 0.01Mhz between different fobs, just enough so your next door neighbour with his peasant farmer's full fat Range Rover doesn't inadvertently fire up the FBH on your middle class Disco 5 on a cold and wintry morning.
There's a naughty trick you used to be able to do with the old style Sky HD box replacement remotes you could buy from Currys or Argos etc, where you could stand on the pavement outside your neighbours front window, pair the remote to their box and start turning their TV volume up and down or changing channels...drives folk mental and they think their TV is possessed.
When I was much younger and we lived in army married quarters...the Sky van was parked outside our irritating next door neighbour's house at least twice a week.
He had the grave misfortune of being a Sergeant Major in the Military Police who, when chatting over the garden fence with a cup of tea as one does to be neighbourly, mentioned his dislike of our regiment at every opportunity. I remember the phrase 'Indisciplined, self entitled hooligans' being thrown about more than once
We were never going to be best mates
.