Let me try and explain this a bit differently as there seems to be some confusion between a ground fault and a short to ground.
If the element shorted to ground during it's heating up period (unlikely, but it has happened in the past), it will likely burn out. A burnt out element should show no ohms reading. Also, if this happens, the 110V fuse at the fridge control module will blow.
Since the fuse (from the info so far) is still good, and the new element shows the proper ohms reading, I would suggest the new element is still functional.
A tripped GFI indicates an intermittent or missing ground, thus the suggestion to check the cord(s) to the trailer.
