[gordner]

The accuracy of the ATC position in this case comes from the aircraft systems, not ATC's radars. So a gross position error on the aircraft would translate to a gross position error for ATC.
Essentially the aircraft nav systems keep track of where the aircraft is and when "pinged" by ATC radar (radio transmission asking for position data) the AC transponder reports the position. Real radar is a transmitted signal going out, bouncing off a target and returning. In this system the outbound signal and the return signal are not the same signal at all, the out bound is received by the AC and a new signal return generated by the xponder.