Unfortunately, water can get in for any number of reasons, but the door membrane does seem to be a common culprit. The only reason I can imagine how the membrane gets 'torn' is somebody cut into it to repair a mechanical bit and didn't properly reseal it. Just shoddy workmanship is the cause. Whether both sides need doing depends on how likely you think this clod was into both sides. OTOH, once you figure out how to get the card off on one side, the other side will be a doddle, so you may as well take a look.
There's only a couple difficulties, one is knowing where all the fasteners are hidden, but there are plenty of online references to help. The other is the top connection can be very resistant to efforts to release it. Depending on the damage, it may be possible to repair the membrane, or just cover the whole door with common 6 mil polyethylene sheeting, glued on with silicone sealant. Or that may be another of my bad ideas? :?