The US is a fucked up place because they want to make sure a babysitter doesn't shake their baby to death or a housecleaner doesn't break or pocket something without admitting it? Hyperbole much?
I mean, if we extend your logic, we should monitor everyone at all times because someone might just accidentally do something to hurt your child right? You never know why an extremely rare event like you mentioned could happen.
Edit: also, cameras don't have to be secret. Knowledge that they're being recorded can often stop it happening the first time.
(I realize this isn't really addressing your intended meaning, but the ambiguity is there in what you said, which is pretty...)
(which obviously they aren't, they are documenting instances where vetting the sitter fails, not keeping marginal sitters in line)
That is protecting the baby's health, which sometimes reaches the level of saving lives.
Your logic only works if camera footage goes unwatched until the day the babysitter exits the business.
Edit: And that 'thin line' remark is 100% a strawman. I don't know how you can admit it isn't the "intended meaning" and yet claim it's not a strawman.