If your position was independent enough, you could maybe get by with a "show me a mistake, and I'll acknowledge and fix it and eat crow. If you are just guessing, go look for an error."

Or if there was storage space enough, make a mirror directory with copies renamed, so there was obviously no loss of original files, then invite them to check as many as they wanted.

I do understand that many people don't trust automation like this, I've been there too.