The most common way of steeling cars, in the UK, seems to be by breaking into the house, or otherwise obtaining the keys. I have seen reports of thievs using a telescoping fishing rod to hook keys from a table in the hallway, through the letterbox.
The code grabbing systems will only work on older cars that don't use rolling codes, or where the thief has a list of the codes, so can work out which one comes next. I agree that this could be possible.
I did work out a simple method of forcing this situation, after I got locked out of a car, as the fob had been pressed repeatedly, whilst away from the vehicle, with car and fob having gotten out of sync. But I'll keep that to myself.
As we are sharing stories....
A while ago, we had a works outing. After the event, we all start drifting off to our cars. But one guy could not get into his.
I have him a spare fob battery to try, but no-go. I suspected that he had suffered the same problem as I had, with the fob getting out of sync with the car receiver and this was indeed the case. So he had to get into the car to re-sync the two. But he had de-locked his car, and the only way in, was breaking a window.
I believe he now has a hidden button or similar to get access if this happens again.
Another one involved a company, who had all their reps/managers cars on lease, all co-terminus. So they decided that their annual meeting would be a good time to change the fleet. All the old cars were signed over and during the day the lease company took them away, leaving the new ones in place.
When the staff came out they found that no-one could open their cars. Techs were called, AA/RAC, lots of fun.
Turns out that the new cars had their key fobs on the new European frequency of 433MHz (previously 417MHz was used in the UK). And there was a radio repeater on the building that transmitted close to that frequency.
Whilst the lease company were dropping off the cars, the repeater was probably not in use, but at rush hour later in the day, it was running and jamming the key fob receivers in all the cars.
Inadvertant jamming is still an issue today. The breakdown/recovery firms only fix, is to tow the car a mile down the road and try using the fobs again.
I play with high altitude balloons, these are meteorological balloons with home made tracking beacons, which transmit on 433MHz. And I've jammed my own car with them amny times. As I can't switch them off, I've resorted to hiding them inside the BBQ down the garden, opening the car, then quickly collecting the transmiter, before the car immobiliser cuts in again. Luckilly the neigbours stopped doubting my sanity years ago.