Rather than a finger print, I'd say a constantly shifting password. A bit like how facebook can generate a security pin to log in with new devices which changes every 10 minutes.
Of course even that isn't foolproof.
But even if, by some magic, they did develop a backdoor that legally had to be put in all software. What's to stop somebody publishing software without this backdoor? Sure a company trading in the US / UK can't, but an individual who doesn't like backdors in their device?