I like your idea of suggesting a mail to all parents to inform them that it's SATs time and to be quiet around the school grounds during the day - at least that way something productive has come out of this
OP as it's SATS, I think this was the best way to deal with it. I would cut the teacher some slack, and leave it this time. (But if i ever happened to be chatting informally to the teacher, I would definitately have to explain that it wasn't my child.)
Until MN, I didn't realise people got worked up about things like this. This is the kind of thing that I probably would not even remember to tell DP about when he came home. Honestly, forget about it. It is such a minor thing
Some people seem to think it's a minor detail but I would be fizzing over the injustice of it
Maybe I’m a bit sensitive, I was actually quite upset by it. It was just a bit of a shock.
I think it's fine for you to be a bit upset or put out by someone shouting at you for something you didn't do and can't control OP.
I'm one of the ones who does get upset about this kind of thing. I can lie awake at night in tears because of it. It's the school setting which sparks the anxiety.
If it happened any where else in my normal adult life I'd brush it off, but in school I struggle.
I know I still need to heal from my own school days, but when I'm in the DC's school and see how adults and kids behave it just sparks all my anxiety off.
(Still fuming about being told off for sending my child in with a waterproof coat in reception, he's 13 now. Still not sure what was I was supposed to have done in the situation)