Thank you brain. It just dished up one of those dreams so perfect and strange and funny I woke up laughing. Couldn't have come up with this stuff through any rational means ...
When Harry Potter first arrived at Hogwarts, he was given an entrance exam (which nobody else had to take). Based on the results, he was sent to the not-so-famous school on the other side of the tracks, called Dumbledown's School. Sign at the gate: "No owls allowed." Among the administrators it was known as Dumbledown's School for Really Inconvenient People. It was a series of really gothic group homes with way too many towers. Parts of the school were just unfinished graphics, and if the kids wandered in there, they would have to go home and wash the pixel dust from their hair.
During the limited school hours, the kids learned how to make Pop-Tarts and Spaghetti-O's, how to unfreeze ice cubes by smashing them with a hammer, and how to remove a dozen types of arcane stains from piles of laundry.
For most of the day they worked out in a peat pog, cutting up little slices of fuel for the big furnace downstairs. If they found any bog people buried in the muck, there was a brief ceremony, and the body was sent to the school medical examiner, who was (of course), Quincy M.E. in a deep purple robe with sparkly bits on the cuffs. Sadly, every case turned out to be a ritual strangulation, so Quincy was writing a treatise on decipher the ancient tattoos.
Instead of quidditch, each group home had a team of sorts, and they get together to toss cow pies. Harry could catch a 40-yard whoozie like the best of them. But being the best of "them" was never good enough for Harry.
One day, while Harry was out in the peat bog, complaining, Hagred came riding along doing whatever the heck Hagred does out in the woods. He fell off the wagon and crushed Harry flat. Harry was such a pancake, literally two-dimensional, they had to take him to Hogwarts to pump some 3d juice into him. And that's how they found out about the "clerical error".
So that's how Harry really got into the famous school for wizards. Snape claimed to know nothing about this, but was unusually prone to fits of dark laughter.
I don't know which faulty neurons fed me this one, but it made my day.