Aha. Smart thinking there.
Another possibility is that one of the parents, or grandparents, is an alumnus or alumna of the Park School. That sometimes leads to preferential treatment. But I think your suggestion is more plausible.
In any case, this may all me moot, legally, since apparently Maryland requires no "asset test" for its SCHIP applicants. (And I'm not sure scholarships are considered assets.)
But taxpayers who can't send their kids to fashionable private schools are entitled to question why they should subsidize families who can.
Of course, this pretty much explains why Maryland has been an economic basket-case for years.