Something is off there. AFAIK active pickups did not exist at that time so you could not have a guitar sending too hot of a signal for an amplifier. If this is the case as opposed to the more common origin story (below) then it would have been a possible mismatch of pre-amp vs amplification settings on the amplifier itself. However that would have most likely blown a tube so again not too likely.
Anyway the most common origin story of distortion is that it originates with a tear in an amplifier speaker cone rather than any sort of electrical overdrive of the signal.
