It seems that the proponents of this technology believe the benefits far outweigh the harms. Why not have a standard generous payout to anyone misidentified by the system. The payout would be funded by all parties involved, store, police, tech company. If the benefits really do outweigh the harms and the compensation is enough, I think most people would begin welcoming the program.

If the system got gamed (people with a history of false positives seeking to be misidentified), fine, it would encourage the technology to improve and eliminate false positives.