The remotes for my car definitely works via radio wave and yes, its range is very short. I actually found out via a foreign Bimmer forum that this is not unique locally.
In the States, the dealer can fit in a remote amplifier to make the thing work better. I even have the part number for this gadget and discrete enquiring through the backdoors of PML actually confirmed the existence of such a part, even though the service people claim they know nothing about such a gadget.
I guess the service guys here at PML are just plain ignorant!