Yes, that's why a two-wire cord on either input or output or both is okay. A three wire cord is also okay but not both input and output.
Well, change that. The three wire cord, if it only adds a grounding wire, is okay anywhere. That way the house conduits and the transformer housing and the load chassis can all be at the same potential, independent of the power line itslf and its current. The main thing is that there be no continuity between either side of the power line and the chassis.
It's true that the house wiring will connect the ground wire to the neutral in most cases. But that should cause no harm and, in fact, keep static potential from building.
In order to make it safe, isolation can work but isn't what is necessary. What is necessary is that the 'hot' side of the line (black wire in most setups) is never connected to the chassis regardless of plug orientation. But isolation solves another problem, any fault from a poor ground.
I had the latter in the case of my bathroom lights and the ceiling room heater. The lights were connected from ground/neutral over to one hot side of the line. The heater was connected from the same ground/neutral to the other side of the power line, so there was 240 Volts from the hot side of the lights to the hot side of the heater. Somehow there was an open in the ground, so there was 240 Volts across the series combination of lights and heater. As soon as I switched on the heater, the lights burned out because most of the 240 Volts was across them due to the low resistance of the heater.
This really has nothing to do with isolation but is a heads up that things aren't always what they seem.