Can the Fitbit sync with a Google Nexus 10?
I borrowed a friend's Fitbit and tried to sync it with my Nexus 10. I enabled Bluetooth. I then installed the Fitbit app and logged in as him. There is no option anywhere to sync the device.

I then logged out, and created a new account. On a compatible device, once the account is created, it prompts you to sync a Fitbit device. This question is never asked on the Nexus 10.

Circumstantial additional evidence comes from the large number of unhappy reviews citing device compatibility on the Fitbit app page.

So it is confirmed that despite the probable existence of the necessary bluetooth hardware/software, at the time of writing Fitbit devices cannot be synced with the Nexus 10.