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Since there's a lot of this kind of thinking, I verified that the app's not connecting, then I went out to the car and got in, and put it in gear. See, there are many different things that go on with the phone. Entry (via bluetooth) will work even if looking at your car on the phone (via servers) doesn't. I also used the browser in the car (via WiFi), and played music from the phone (bluetooth again, but not the same connection that unlocks the car...). Looked at the supercharger map (WiFi again) but I don't know how to tell if it's current (nothing greyed out, though). Oh, and now the app just came back up.
you don't need tesla's servers to be up to use your phone as a key. As long as your phone is paired to the car via bluetooth (LE), you can lock/unlock it and drive it.