Do you honestly believe facebook won't look for and find ways to encroach on privacy more than currently available free wifi does? Their entire mission is to encroach on privacy, and now they've got you connecting to their wifi hotspots at the gynecologist's office.
Actually, it might very well happen that these Wifi networks all have the same SSID, which would likely make most devices automatically connect to them.
Even if they don't, they only ever need one connection to link your device's MAC to your username, and then detect it without ever connecting.
