an isolation transformer doesn't magically make everything safe;
No, it makes one specific action safe - i.e. connecting a grounded 'scope lead to an arbitrary point in the DUT without letting the magic smoke out of the DUT or your 'scope.
It's best to think of it as a device that protects test equipment (from the specific action above) - if the operator finds himself connected between two points in the DUT with enough potential difference between them life will become painful, short or both depending on the impedance of said PD.
Also, having provided a new ground reference for the DUT it becomes possible to complete a circuit by touching a single point in the DUT if you are also grounded. Again if there is enough voltage and low enough impedance life becomes,..... well you can figure that bit out yourself
More embarrassingly the single point of interest might be the chassis.
Eg consider an audio power amplifier with ± 100v rails. OK, connect it up to an isolation transformer and ground the -100V rail. You now have the "0V" rail 100V above ground and it's likely the chassis is connected to 0V - enough for a nasty nip. The +100V rail is now 200V above ground, enough to kill considering this is DC and the PSU will probably be capable of several amps.