The TV repairman probably does end up grounding the set through the test equipment. It is very common for line-powered oscilloscopes to have the signal ground connected to earth ground, for example.
Yes, and as all the signal circuits in the old "live chassis" sets are tied to the supply, we need to use the isolation xfmr for that very reason. First, if the polarity is reversed the chassis will actually be hot and obviously connecting a grounded scope or meter probe to chassis will set the sparks flying.
But even if the chassis is to the neutral, you still don't want to cross it with true earth ground and create a parallel path. That could result in neutral currents from other loads flowing through your test equipment grounds.
