I would not use the welding idea is like saying you would not drive the car because you might wreck. Anyone that welds knows that weld will spatter and you shield those things that it can damage from that spatter (especially glass), plus ground the car. It is not the only answer to a problem but it is an answer to a striped out, and at times, rusted on wheel nut, lock or otherwise.
In this case he has 4 problems waiting on him and most likely his best path of correction is to obtain the proper tool for when the other three need attention.
It's not internet lore, I've done it, didn't damage the wheels, nor did I burn the car or the building it was in.
Think and work safely when you do any task, which includes driving.