Isolation with inverter
By regulation in most cases offline switchers have to be isolated. Inverters are typically isolated as well.  However, a floating scope is a safety hazard. Suppose you put your ground clip on something at 500V potential. Then you pick up the scope probe for channel 2 while touching the case of your lab supply (for example) and come into contact with the barrel ground or ground clip. You probably wouldn't like the result. Better to use a real differential probe.