So, I really do not have a horse in this race, and I am on thin ice because I am not trained as a mechanical engineer. To re-state the original issue I was concerned about the bare metal lying between the mounting holes pressing into the painted surface and damaging it, thus potentially allowing water to create an issue.
It seems to me that this mini system (the handle, bracket, backing plate, pivots and springs ... etc) is strengthened because the bracket, AND its backing plate behind the door skin sandwich the door skin. My backyard logic would suggest that all the forces involved with lifting the handle are distributed because of the bracket and the backing plate. Again, backyard logic, if you separate the bracket from the skin it seems to me you change the mechanical system and the skin no longer supports the bracket and backing plate in the same manner, and I don't think it improves the distribution of the force involved. So, to me anything that puts air between the skin and the bracket (a washer of any type) may not be favorable. A strip of hard plastic between the door skin and the bracket sounds better than bare metal but will probably injure the softer paint surface. Again, backyard logic, the thin rubber was meant to be sacrificed to protect the paint, and allow the forces at play to remain relatively unchanged, at least in my own mind. The entire bracket surface is still in contact with the door skin. A thin piece of soft plastic might be better than rubber, because it might be more resilient against the elements, but I am not sure that it would fail before the paint. This is a fun topic because it is more complicated than it appears at first glance. If there is an ME or structural engineer out there this would be a good time to explain what is really going on.
My final thought, at least for this reply, is that the bucket is 43+ years old. When we acquired it a number of systems had failed, including seals, rusted metal, ... etc. The metal under the door handle was not a problem. I also do not remember anything remarkable about the paint on either door in this area. My point is that without realizing it I may have started a red herring. The Datsun engineers must have done a pretty good job - it lasted this long.