That sounds a bit far fetched to me, I have had my Internet go down multiple times and never have a Nest problem. In fact I don’t even think an Internet connection is required if you just want it to be a dumb thermostat.
The default safety settings on my nest is 45F for heat and 95F for AC. This setting is user adjustable so maybe your family member override it.
You are probably in the US. In Germany usually each radiator has a thermostat and you usually do not have wall thermostats unless you have floor heating.
That being said, I’ve double checked and it is Netatmo [0] and not Nest. The point still stands, that some cloud based home automation devices behave stupid if they cannot talk to the server.
The default safety settings on my nest is 45F for heat and 95F for AC. This setting is user adjustable so maybe your family member override it.