sounds like they used a cycling transponder scanner.
the machine runs through loads of transponder signals until it locks on to the one for the car, then unlocks it. its enough to get into the car, but they can't start it as they won't be able to get past the emobiliser.
old school method, there used to be a watch that you could control your tv with, to lock the signal you used to set it to scan while the tv was used on normal remote. it stored the code and then you could use it normally via the watch.
they may have done something similair, been nearby when you got home and locked up and stored the infared code. then reused it while you were asleep.