All access doors and hatches can be the source of leaks - in fact, any opening in the hull. Any screw hole placed in the wrong spot can be a leak.
There are two basic types of access doors - those wirh rounded corners, and those with angled corners. They can leak in the same way that windows do. In addition, they have seams where the different parts of the frame meet that are usually not sealed and can allow water intrusion, especially at the lower corners of the angled doors.
The older types of campers with the corrugated aluminum siding are -imo- more prone to develop leaks around access doors or windows. There is no flat surface to seal, and the seal / caulking has more difficulty to brigde the gap at the lower ridges of the siding.
Keep in mind that water runs downhill and may collect in a well sealed low spot. The location of the water damage does not neccessarily indicate the location of the leak.