That would be true for a line powered device that has no internal isolation transformer...................... there is one situation in which this configuration will be an issue if the device under test also has a safety ground and that safety ground is also tied to the device's circuit ground. Connecting such a DUT to the variac would mean the DUT now has a mains referenced ground even if the variac outputs are isolated from ground. ........................
But the main reason for using an isolated transformer, as being discussed here, is for testing such a line powered device that has no isolation, and such a device should never have its common tied to the safety ground.
That's a strict no-no since neutral and the safety ground should only be tied together at the main's breaker panel.
For example, if the hot and neutral are accidentally interchanged at the plug with the (supposed) neutral wire tied to ground, then the hot will be shorted to neutral.