I'm gonna call shenanigans on this tweet until seconded or proven otherwise. I have a Nest and have not seen that at all.
That user may have been asked to accept new Play store conditions on an Android device before using the app, but I don't think that has anything to do with the acquisition.
I think that was a joke. Nest's terms haven't been changed (has the acquisition even completed yet?), and neither the web or mobile app has asked me to agree to anything new. The app is just a remote control -- so the "to heat my house" is hyperbole. The thermostat doesn't require internet at all, let alone an app, to heat the house.
Even if it were true though, why would that change your opinion? A TOS revision is inevitable if only to change the company name and address. Do you think that Nest didn't require agreeing to terms of service before using their app in the past? Or that any manufacturer makes a mobile app for a connected thermostat that doesn't require agreeing to terms of service to use?
More, but not really because of who has what number of dollars. Honestly, I've been interested in them for a while, but the acquisition news made me interested enough to stop and play with one. They're pretty damn awesome pieces of hardware!
More. I feel better buying one because I know a big company is funding the development. Also I expect the prices to fall as they take advantage of the economies of scale with better brand recognition.