For the most part, yes, though I don't think it is particularly unreasonable to expect that you could view some of your recent activities in the app without having to phone home, given how small the .FIT files tend to be.

Syncing with other apps is also something I would expect could be done without phoning home, assuming the other app is capable of parsing your .FIT file directly (which Strava is). In that case all the app needs to do is fetch the .FIT over Bluetooth and pass to the third party app using whatever phone API.