As long as the wires from the new button are connected to the same wires on the solenoid that the stock starter button wires were connected to, it should be fine, if a little lazy on the part of the PO. If the wires are connected directly to the main terminals on top of the solenoid then you've got yourself a crazy PO.
If they were connected to the main terminals, though, it probably would have fried the button assembly on the first try.