Years ago I learned the proper way to drill out rivets in aircraft skin ensuring that I didn't have to go oversize. It's all about finesse using the drill, with the drill rotating slowly, move the drill to keep it centered until you have an established drill start. If you attempt to apply full power to the drill with out finesse, then yes, it is easy to lose your center and the drill bit will wander possibly taking out some threads. I have found that by exercising extreme care, using the drill at slow speeds and finessing it you can keep the drill on center and drill a hole straight through the middle. Use a pilot drill first, if drilling out a 3/16ths bolt I would use a #30 drill. If the easy out doesn't work for you take the hole out right up to the ID of the hole and pick out the remaining pieces with a dental pick and run a bottoming tap back through the hole when done.