Ours is a Dometic RM2333 and I'd suggest the following:
1) Find a way to make sure the water is actually coming from inside the frig, not from underneath suggesting an unrelated source. The rust doesn't compute with me somehow.
2) If from the inside, does yours have finned cooling element on the top inside? If so the fins are probably condensing moisture from the air and dripping down to the bottom. On mine, Dometic suggest that when operating the fins should have a dry-ish frost on them, but that would vary with the setting, the frequency of the door opening and other variables, including variations in ambient and inside temperature.
3) Mine has a long rectangular plastic drip pan which fits on the bottom right under the fins. Occasionally it should be emptied out. If yours originally had a pan I'd try to get one, but something could easily be improvised I'm sure.
4) Get a wireless (Radio Shack) thermometer. Mount the sender inside the frig and monitor the temperature from the outside, the car, or your home, whatever. Very handy, but you may discover, as I did, that the installation was faulty and the frig did not function as well as I thought it should. I'd be happy to share my experience with this problem as well as some remedies, but yours may very well operate just fine.