Damn. I like my Fitbit. I wouldn't be looking forward to having it stop working with no notice because Google decided to just shut down the servers on a random Tuesday and shutter the product line...
Yes, as it works right now. You can't sync it to your phone. (through your phone). You sync it to their server and your phone also connects to the server.
There's presumably some caching on your phone, but the server is the source of truth, and I don't think you can get updated info on your phone without it round-tripping to their server first.
