It sounds to me that you (or Uspensky) are trying to define "proof" to mean all good things.

I don't understand what that means, and what exactly do you think it's wrong with the definition offered. Certainly it doesn't encompass definitions, axioms, conjectures, intuition, background knowledge and other good things in mathematics.

I know and value Thurston's paper, and again, don't quite see the relevance.