They could be still over in US, they could be here. I suspect over here, but I wouldn't be totally amazed to find they aren't. They could easily be registered with an online school when they could work from anywhere, or they might have a (or more) tutor who travels with them. I doubt their parents have even considered doing it for heaps of reasons, not least that they're far too important and busy to have time.
What information has been put out?
Photo of several cars leaving B'ham airport - could be anyone in there
Various announcements hinting at what school they've chosen - there's enough information for people to make confident guesses, but if you were at one of those schools and you knew they weren't there, you'd just assume that they were at another and guesses were wrong.
"Announcements" from the school in question. These seem to have come from HAM, even if you believe they exist. Again, because the school hasn't been definitely named, no one will bother denying it.
Saying when they're starting school.
Announcement from HAM that everyone loves them and it's all wonderful and they've joined the WhatsApp group
Leaking of the WhatsApp group screenshot - HAM again
A video made to look like it it was filmed here after they'd arrived in the UK in August, but more likely filmed at other times.
They're all things that make it sound right, but don't actually give any true information. They're either clearly desperate for the school to be leaked, or they want to give enough information to make it sound plausible with no actual proof.
There's a few little things as well - Hello reported HAM as having settled Lili into Reception class, obviously coming from HAM. I thought she was 5yo, in which case it should be year 1? Now it is fairly usual ime for those coming over from US to have to drop a year, but I can't see HAM wanting that for their amazing daughter. I'm sure they would see it as infra dig for their dc.
I doubt HAM would know offhand the school starting age was 4yo in September, but often people say "school starting age is 5yo". So if they hadn't actually put them into school, they probably would assume that she'd be going into the youngest form - reception, because they wouldn't have been corrected by someone who knew.
In fact they've done fairly much what I would do if I wanted to lay a trail looking publicly like my dc were in school when they weren't.
I'd probably have added a "back to school" photo. They could have done one with them in cute long woollen coats with just a peek of Archie's shorts showing and long socks from behind which could be generic posh school. Or waving from the window of the car, or after coming out with tie and jumper taken off and messy with paint is perhaps more their style...
And I'd also have placed someone to take a photo of a convoy and put it on a village FB chat. "Anyone know who this is? Not seen this before." Actually send the convoy through and you'd get plenty of "I saw it too", although if it was our local chat the stories would probably have had them robbed the local pub and squashed a cat by lunch time. Safer not really to do so then. 🤣