It's no different to companies choosing not to do business with people based on credit history, financial standing, etc.
Or, perhaps I'm just suspected of shoplifting because one of my friends did shoplift while I was with them, and I'm added to the list. The doubt is reasonable enough that it wouldn't get me convicted, but it's enough for this system to add me and keep me in it.
For the rest of my life, I would be treated as a criminal by shopowners, even if I never commit another crime.
If they opt for a stricter system (which would cover the edge cases you describe) that loses them some genuine custom, that's their loss.
The target is of course persistent offenders, not the kind you mention.
Also, I could be badly mistaken, but isn't slander strongly enforced in the UK? Wasn't there a scandal involving forced apologies?