Thanks! See, that distinction is super helpful. I've found (old) lists of Smart TV OSes and how their privacy settings work (or don't), with some details on what happens when you decline EULA's, but not many and not very useful ones.
The answer may well be that anyone that actually cares about this stuff just doesn't buy any smart TV (or otherwise hasn't had to in the last few years). Still, with the answer 'just don't connect it to the internet' being the most common, I'd expected to see a bit more information like you've given.
So the Samsung keeps nagging even when you're watching direct HDMI input? And does the LG need to boot up the entire (Web)OS to view HDMI input?
I get what you're saying. What I'm running into is that there is little information on what happens if you 'dont connect it to the internet at all'. I would happily do that, but as another comment notes, some devices keep whining until you do connect them, while others don't. I can also easily set up a separate 'fake' network to black-hole all the communication attempts of the TV, but I have no idea whether that would stop the nagging -- or the attempts for it to connect to public WiFi access points.
It would be really cool if people experimenting with this kind of thing could pool their findings, that's all.