If you connect your Fitbit account to Facebook for the purpose of friend-finding, Facebook may keep track of your being a Fitbit user. However, Fitbit does not connect your device to Facebook. The possible exception to this is if you have a smart watch from Fitbit and a third party app establishes such a connection. Fitbit does not act as an intermediary here and so cannot keep your information private.

(Disclosure — I am a Fitbit engineer.)