Mains (in almost all cases) has Neutral and Live and, when present, safety ground.
Safety ground and Neutral are connected somewhere close to where the mains comes into the building.
This means Live has a full voltage opposite ground you walk on, safety ground and Neutral.
Touch Live and you get a jolt.
Touch Neutral and you won't (there might be a very low voltage opposite ground).
When run through an isolation transformer you can touch the 'Live' out and not get a jolt. You can touch the 'Neutral' and not get a jolt. You can touch the safety ground and not get a jolt.
Both isolation transformers will do the same thing.
The point PMA is making that when you do have a ground loop the discussed Tripp Lite won't break that where a double insulated one will yet loads are safe to touch in both cases. In the Tripp lite version it is ensured by safety ground in the double insulated one because the output mains voltage 'floats' and is not referenced to ground so no jolt and no ground loop.
So there are no different opinions just different devices doing the same except for safety ground.
Sometimes, certainly when switchers are used, a ground loop is not because of different voltages between safety ground but is caused by 'leakage' though the mains power supply. This can occur with switchers that, in order to comply to FCC rules, use a Y cap between Neutral and the DC output when for some reason N and L are swapped for instance. That current is very low (you may feel a slight tingle) but can be high enough to create a voltage drop across the screen of an RCA cable.
An isolation transformer with safety ground can still solve the problem with such a loop (think computer power supplies).