It's not so much the high current from welding that damages electronics, although that is a factor, its the huge magnetic field that is created by the very large current. This magnetic field actually moves small things around, like wires and the innards of transistors, so even a coil, with its very fine wires, can be damaged.
Now, some good ole boy who has been welding for 45 years will chime in here and say that's BS because he has never had a problem. Sure, Evil Kenevil didn't have too many problems either, but I wouldn't do what he did. Would you?