I would disagree with the implied dichotomy of 'criminal minds' and 'non-criminal minds', especially given the somewhat arbitrary nature of what we as a society decide is a crime worthy of prosecution. Possessing a bit of home-grown marijuana for personal use can give someone a criminal record the same as other more heinous crimes, and many employers will find it easier to blanket-reject anyone with a criminal record rather than dig into the context of each applicant.

Is the answer to not allow any sort of background checks? I would say no, but it also seems like there is a lot of room to improve our current system and find it in our societal heart to not perpetually punish a person for a past minor offense.