We Don't agonize over Lily, Freddie, George, Ben and the rest of them, rarely hear about parent evenings, school plays or academy status etc.
We did have a bit of a storyline about which school Lily and Freddie should go to, didn't we? (Elizabeth didn't believe in private education; Nigel did.) I think there was something about Dan and the Cathedral School, and wasn't there a chance of Pip getting a music scholarship there, and taking after Phil musically? (When did we last hear a hint that Pip's at all musical?)
So I think that while we don't hear much about Ambridge children once they're at school, we do get quite a bit about choosing which school they'll go to.
Also, while it's a pretty small proportion of boarders in Britain, there will be areas of the population where it will be higher - this includes children of people in the forces, but I would expect it also to include children from the land-owning side of agriculture (rather than the labouring side.) So it would not be unreasonable for parts of Ambridge to at least have secondhand knowledge of boarding, if not first-hand.
SOC could at least learn to google.