Sorry my reply wasn't clear, I understood the question you were asking in your original comment. I was actually referring to your 2-edge protocol when I wrote t

Sorry my reply wasn't clear, I understood the question you were asking in your original comment. I was actually referring to your 2-edge protocol when I wrote that it seems the Verifier could not be tricked even in the simulated protocol (since it could detect inconsistencies as you mentioned). I think the theorem says that if your Solver can successfully trick the Verifier in the simulated protocol (aka using the rewinding trick), then your protocol is zero-knowledge. But I'm really not sure... Let me know if you find a more satisfying answer.