The scope gets an unusually large current flowing through its earth connections. but that's normally BNC terminals to the shielding case and the case to the mains earthing wire. Not through chips or components so it usually doesn't damage the scope.
I think my original confusion and why I initially posted the question was due to always hearing the scope can blow up. Normally I attach the ground lead to chassis ground, and, if it's obvious that is an isolated ground, I seek the negative/return. Most of my high voltage measurements have been at most AC input, but the majority are always low voltage secondary transformer side measurements. I have measured AC directly across the plug, but always make sure I know which side is neutral before doing so (I actually found a receptacle in my house that had a reverse HOT and NEUTRAL by way of one of those cheap LED testers that plug in and give you a sequence of lights that show the state of the receptacle - so it's not safe to assume that NEUTRAL is actually correctly connected).
My confusion came because I know the ground lead is Earth ground and touching a "hot" will cause a short circuit, but, the more I kept hearing that the scope can blow up, the more confused I got about the so called ground loop. Ignoring the scope probe blowing up in my hand, and blowing up the DUT (or hopefully the fuse first), I visualized a scenario where touching the ground lead to the wrong point will cause the scope to float so high that the internal electronics blows up due to nothing more than it floating. This doesn't seem to be the case. From my understanding, providing I keep the voltage below the maximum input voltage (400V ?), the scope isn't going to simply blow up because the ground lead floated (ignoring that I'm shorting a point to Earth ground and something will blow up).
As usual, maybe I over thought this and didn't need to ask the question. A very common situation is a power supply with three prongs, the scope with three prongs, scope probe ground lead touches a "hot" point, the fuse blows on the DUT, and nothing bad happens. A theoretical situation I imagine is that the instantaneous current is so bad that it blows open ground etches and pathways to ground in the scope causing the electricity on the point inside the scope that just opened to seek a path to ground and finds it through an adjacent IC chip thus "blowing" up the scope.
As for floating the scope, electronics that have ground points floating above ground, high voltage power supplies, etc... these are most things I stay away from because I don't grasp enough about grounding to feel safe gambling with anything (or being around high voltage especially if I'm alone). Sometimes "Earth" ground makes sense to me, other times I get confused. In some equipment, such as a weed wacker, Earth ground is a secondary grounding source to avoid being electrocuted should the neutral open but you won't get a shock should the third prong go missing. In other stuff, such as maybe a refrigerator, with the third prong broken off, the device will give you a shock. Rhetorically asking, why does one pose a shock risk and the other doesn't?
A silly question: why not install a PICO fuse in the ground lead so it opens before (hopefully) any injuries occur or damage to the scope?
Regarding differential probes, I assume they are not bullet proof meaning measuring something you shouldn't can cause an arc thus taking out the scope. In any case, it seems using them is certainly the safest method, however, are they reducing signal quality/bandwidth?
If my scope probe is some high end HP going into a high frequency scope (my four channel is 600MHz), and I use a diff probe, then I'm reducing signal quality.
What about measuring voltages without the ground lead connected, can this cause the scope to blow? Sometimes I've measured signals where it didn't make any difference whether ground was connected or not, but I assume the connection was through Earth ground.