Well, it was a joke, but to take an earnest question seriously, there are entrance exams, but they're not especially hard, particularly if you've been coached beforehand, as many of these kids will be. Theoretically no special cases, and "celebrity" would certainly be frowned on at Eton / Harrow - these are old-money families, not nouveau-riches.
The funny thing is that this entrance exam to Eton is effectively their ticket to the top, once you're there you're on easy street. Boris Johnson attended Eton, didn't achieve particularly good results but cruised into a scholarship at Oxford. I attended a decent state school and had a fellow student who had literally top grades in all the exams he'd taken (eight "1"s at Standard Grade, five "A"s at higher, five "A"s at Advanced Higher) and his application to Oxford was touch-and-go. Now, such grades do not guarantee anyone a place at Oxford as there is a lot of competition, but you can be sure that if he had two English A-levels at grade B or C[0] he wouldn't even have been considered. The application would go instantly to the bin.
This is not true of Eton (or I guess Harrow or the other public schools).
[0] - Or whatever Boris Johnson got, I can't recall exactly, they were spectacularly subpar but he's masterfully scrubbed them from the internet
I edited the comment — “celebrity” might be the wrong word, but I was thinking that they might care more about having a noble’s kid attend than the 45k, and, like you just implied, they’d reject nouveau-riches even if they had the money, especially if the riches came from a source that’s frowned upon.
So it’s not a very good joke, as it implies that there aren’t any other filters, despite their intense concern for reputation.
They need to have enough truth/insight to be funny. When your premise is that Eton only looks at cash-in-hand for admissions -- pretty much the opposite of the truth -- that doesn't qualify.
The joke would only work for schools that famously looked the other way on pretty egregious stuff if you paid them enough -- not on a school that makes a point of heavily filtering beyond the official tuition. (Sorry, "sticker price".)
Side note: It's also kinda funny how the parent expects 45k to be some kind of jaw-dropping, outrageous number, when Americans routinely pay that much for college.
