But is there ever a circumstance where a 'good' tube will cause the
shorts light to light? I ask because I had some 6146s a while ago that
would light the 'shorts' light up, but tested far into the 'good' range
scale.

One of the calibration steps in the manual is to set the "shorts"
sensitivity, using a 1 megohm resistor. Power tubes are allowed a
little more leakage than receiving tubes, so could exceed the "shorts"
threshold and still be good.

Alan