Yeah, it's a bit ragebaity. Afaik the solar panels can be "turned off" (disconnected from the grid/open load) just fine, and there absolutely needs to be a way for this to happen automatically (a proper smart grid).
The big power plants are another story.
The first reauui found is kinda interesting
even conventional diesel generators have this issue https://www.cat.com/en_US/by-industry/electric-power/Articles/White-papers/the-impact-of-generator-set-underloading.html
Yep absolutely
a few kW? I can burn that no problem. A MW? Well...that takes a little more thought. A GW? That's a whole different ballgame.