So this happened again (but with an exciting new twist).
My second goddamned Samsung Gear Live broke just the same as the first.
My attempts to get it repaired/replaced: http://j.mp/brokenLive
tl;dr:
Google won't replace it but they will screw me around for a few weeks before telling me.
Samsung won't fix it but they will re-direct me to a third-party repair center who will sell me a new one.
Don't buy these things.