[Refugee]

An isolating transformer allows the DUT to float so that one point in the DUT can be earthed for example the negative of a mains rectifier.
With the DUT connected and nothing else you will get live mains through any capacitance between the windings in the isolating transformer. This will show on a DMM.
If you connect the chassis to a scope earth and then touch a high voltage point in the DUT it will bight you as you have effectively created a local earth in the DUT.
Isolating transformers became a must have item in the days of live chassis TVs and normally accompanied the scope in TV workshops.
Your amplifiers all have isolating transformers and earthed chassis in them.