First of all, a bike can be ridden fairly safely without a rear brake. I put over 20,000 miles on a Honda Rebel 250 with no rear brake. It was not intentional. I had fabricated parts to move the footpegs and shifter 6" forward, to give me more room, as the bike was considerably too small for me. I had started to fabricate a new rear brake pedal and linkage, but never finished it, because I had no trouble riding without the rear brake. The Rebel is not a sport bike. In a faster than normal stop, almost all of the braking is done by the front brake, and because of the forward weight transfer, there is almost no weight on the rear wheel. Just touching the brake can lock it up.
However, if the rear brake releases as soon as you release the pedal, it should not be unsafe. If the brake locks up, and won't release, you're in trouble. Same thing if the brake does not operate in a linear fashion, if it goes from barely braking at all to sudden lockup with no or very little extra pressure on the pedal. The front brake on my Kawasaki Vulcan 750 had this problem. It was virtually impossible to control under hard braking, it locked up every time, without warning. It was a dual disc setup, and I solved the problem by removing the entire brake from the right side, leaving it with one disc. It then performed perfectly. It could be locked up, but actually took some effort to do it. Normal braking was uneffected. I have put almost 60,000 miles on the bike after that modification with no issues.
I am not a motorcycle mechanic, but I worked 36 years as an auto mechanic. The brakes are very similar. I believe Steve's problem is caused by the brake assembly itself. I don't see how the swingarm or suspension could have anything to do with it. It almost has to be something to do with the way the shoes are contacting the drum. The harder the shoes contact the drum, the more friction is created, up until the shoes and drum are locked together. Any rear brake can be locked up, but you should have to push pretty hard on the pedal to do it. I sure wish I could get a look at the actual parts. I realize the bike was in an accident, but any accident damage to the brake should be obvious. Not being that familiar with RE (yet) I wonder if all the parts are the right ones, and if there is any binding anywhere, including the pedal and linkage. It should take only a slight motion of the cam to force the shoes against the drum.
As I posted earlier, mine was not working right, I had it completely disassembled, centered it, and properly adjusted it, now it works fine. It's a very simple setup. Hard to imagine something wrong not being obvious.