normal bench tests do not work
Your comment regarding the bench test make sense.
As a rule, normal bench tests do not indicate regulator failure in that they will show the regulator as OK when it is not. This is because the regulator listens for some sort of Pulse Width Modulated signal from the engine computer rather than a conventional voltage signal from the battery and a bench test with conventional alternator test equipment is not designed to test the PWM signals.
There is also a sort of fail safe circuit feature within the regulator that defaults to about 13.3 volts, hence I suspect the bench test showed a constant 13.3 volt output. If so, that is the indication of regulator failure, and yes, the alternator itself is most likely still OK.