A GFCI is a magic charm that protects from all harm

But seriously, you can get all carried away with this stuff and start doing things without good understanding of when they do or don't help. So it's good to be skeptical as you are being.
Fundamentally, you don't absolutely need even an isolation transformer, as long as you keep track of where your grounds are and be aware of what's live in your circuit.
You need to know that ground on the oscilloscope is tied to mains ground. So you must either attach the ground lead of the probe to something that is already connected to mains ground, or attach it to something floating and isolated. But as soon as you attach that ground probe to a floating circuit it won't be floating any more, it will be ground referenced--you have just neutralized your isolation transformer

There's a saying in the workshop, "measure twice, cut once". Similarly in the electronics lab, "think twice, before you attach that probe".
Also, it is often a good idea to clip probes to test points with the device turned off, before turning it on. That way, there is no danger of your hands slipping and touching anything live, or shorting something out.