I see outboard of those door seals (pressed in across the bottom of the doors), have what feels like 3 evenly spaced weep holes. That would seem to be the way the doors *should* dump any accumulated water that gets in them (however it got in there). Maybe those weep holes are plugged up, and water (that finds a way to get in there) starts pooling up. If the water were to rise to the level of the moisture barrier wrap attached to the inside of the doors) and finds a week spot (in that attaching adhesive), it could then start leaking down (inboard of the door seal) and start attacking your carpets.