To be very clear, in any case that I've heard of you power company can't do that unless you sign an agreement and connect your account. (I don’t mean legally, I mean they don’t have the ability to do so technically)

Stories you see in the news of this happening are quite commonly people who got a free/discounted smart thermostat under an agreement that explicitly calls out that the power company can and will (within some limits) turn your thermostat down during overload events. Usually this comes with explicit limits too, I remember verbiage like "up to 4 events per <year/season>, down to <some min/max temp that wasn't really that extreme> and during X to Y hours." Connecting their account is a condition of getting their rebate, so people click-click-click/tap-tap-tap through the agreement without reading because they want "Free stuff."

My thermostat prompts me a few times a year to sign up for the local utilities load-shedding promotion for some $50 or a Homepod mini, etc. I just refuse, I don't have to. (I do try my best anyway to be a community minded person and follow their news announcements - set my thermostat down manually if their is an imminent grid overload.)

I quite enjoy the simple utility of being able to adjust the thermostat or run the fan from bed, or while out of the house. One of the few actually useful smart appliances.