Someone at work in a customer-facing role is less free to handle these things like they want to, potentially at the risk of very real consequences to their job. If you work at a bar, or a mechanic's shop, or in the grocery checkout, a customer throwing a fit and spitefully getting your boss/management involved can lead to anything from straight up losing your job to just being a "difficult" worker and not getting the shifts you need.
If the people are not total strangers, it's different, but approaching someone that didn't volunteer to be in the situation, and can't freely respond, is absolutely inappropriate a lot of the time - I'd argue, at least.
(Obviously, a good employer should help you feel protected and safe in situations like this - but we all know that is not a choice many people get to make for themselves)