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I would never say such a thing publicly... 
With that said, it would be shockingly cruel to disqualify someone from life-enhancing opportunities on the basis of an arbitrary comment and with no further context. I would hope these strict standards would be in place for all applicants, and not just me.
You could also read your post from the outside looking in. Imagine you are a recruiter or hiring manager. Do you think you want to bring someone on who thinks, "I should've been teaching the teacher". Someone who says things like that might not be the type of person others want to work with.