My girlfriend tells me similar stories of when small children are the first time at their dentist office and their parents behave the same as described in the parent comment. The parents are even informed on how to behave but some still can’t stop projecting their fear onto the children with their words and behavior.
As a father of 2 little children I can tell you you're constantly being judged by people around you for for not doing good enough a job parenting - especially by people who aren't parents themselves but think they'd be much better at it. In these situations there's often a lot of background information the casual observer simply has no way of knowing.
Just saying we should maybe give the parents in the anecdote above a bit more benefit of the doubt before judging how wrong they handled the situation.
In the story above, the only explanation I can think of is that the boy already had a previous bad experience with a hairdresser. (Didn't look like it but I can't be sure.) Even then, I'm not sure this was the best way to handle it.
children with autism often react badly to hairdressers. There can be all sorts of reasons for some behavioral pattern.
One day, my nine-year-old child spontaneously developed acute anxiety of car rides. She had ridden in cars daily for years prior to that. Long road trips, everything no problem. And then, out of nowhere, it was a source of acute—we're talking screaming and crying meltdown—terror. There wasn't a single negative car experience that led to it.
Emotions are complex and kids are highly variable. I'm glad you got lucky with your kids and haircuts (mind don't mind them either), but not every emotional experience with kids has a simple narrative explanation.