My wife is a primary teacher so I do get to hear about what happens the other side of the fence a lot.
Teachers are put in absolutely impossible situations. Lets face it, some parents are crap and should't be allowed to have kids, some of the things I've heard are just too horrible to possibly even imagine.
The basic problem is parents not supporting the teachers or their school, for instance this lady probably screamed at the head teacher and threatened she was going to call the police for intimidating or threatening her boy. It doesn't have to be true, parents are often worse liars than the kids. The head teacher probably wasn't in a position to see what really went on and so is probably going by what this lady said and then possibly hearing the mans side and then deciding to play it safe.
What can they do? If some sort of accusation of a threat has been made then take no action and they are dammed, take action and they are dammed too.
My wife's had to sort out lots of problems between kids which are usually quite easy, then deal with the problem between parents, which is often much more serious and out of all proportion to the incident between the kids.
My best advice is to follow their request where practical, but if somebody is hitting your child, by all means ask the other child to stop!
She had one problem recently where she had an excitable and boisterous but basically sweet natured boy who was always playing with another boy and together they would get a bit rough and a few times the other boy was hurt during the rough and tumble. The mum of the other boy interpreted this as the other boy bullying her son (which wasn't the case, it was usually the other play initiating the play!) and so started a vendetta against the other lad. She basically spoke to all of the other parents about the 'bully' in the classroom and lots of the parents banned their kids from playing with him, anytime there was something in the playground with this boy regardless of whether he initated it or not she used it as ammunition and was basically bullying this lad in the worst possible way. It got the point the school had to call the parent in to see the headmaster, crazy really!