While I won't assert that no one needs support (for their testicles), I'm of the opinion that the vast majority don't require it. I've always - since high school - run w/ nylon shorts w/o liners. No problems!
Running nude is even better. I now have an 8 km route through our farm and into the provincial park that surrounds the farm on 3 sides, which I run nude throughout the summer a couple of times a week. I do other, longer training runs on the surrounding public roads - w/ unlined nylon shorts (tights in season).