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.