You can also test your professor's answers. I don't just walk around going "Oh, Claude was right", I'm literally using what I just learned and am generating correct results. I'm not learning facts like dates, or subject things, I'm learning laws, equations, theories, proofs, etc. (Like how to apply Euler's totient or his extended theories on factorization... there's only one "right answer").

Also, you method for attesting your professors accuracy is inherently flawed. That little piece of paper on their wall doesn't correlate with how accurate they are; it doesn't mean zero, but it isn't foolproof. Hate to break it to you, but even heroes are fallible.