No, I don't realise any of that, because Let's turn this device into a secure token is the sum total of the information you get when you fire up the Authy app. No links to any explanations of why they want you to have an account, and I didn't care enough to go looking further myself.

But the real issue for me is: given a choice between (1) having my private tokens physically only on my own devices; (2) having an account and apparently some form of my tokens at a third party in another country susceptible to bulk espionage and subpoenas... why on earth would I choose (2) in today's climate?

Or in summary: I guess I don't trust them to actually encrypt anything in the face of legal threats.

Authy necessarily has the keys on its servers in cleartext. When you integrate them into your application, you send the code the user inputs to Authy's servers for verification.

Authy is a third-party authentication provider, it is not simply a synchronization service.