Would it be okay to have a dog on a tie-out if the dog was supervised the full time?

Sure, no problem. The 3 main problems with tie-outs are (a) that the dog could get caught around something or even strangle himself, (b) that the dog is a sitting duck for stray dogs and mean kids, and (c) that it often means the dog is ignored for hours on end. But if you are there to supervise, all 3 problems are taken care of.