The existence of even a mechanism for secret extradition requests is itself unsubstantiated. Without that, the burden of proof is still on Assange to substantiate why we should expect to be unable to find any proof to support his claims.
For Assange this is a life and death situation. Sure the US will have to promise not to execute him, but nobody can stop them keeping him in conditions where he wishes he was dead. Just ask Manning. So I maintain that Assange is acting rationally regardless of whether he is "right" or "wrong".