If they excessively quote the original letter in their reply, it's not real. Nobody puts this amount of effort into a rejection when they are obviously being mocked by the sender. They would send a generic "not what we're looking for" rejection letter at most.
If I were an admissions officer and got an application like the one hinted at I'd probably put the time into a rejection like this since it's clearly what the sender was really after. I mean, it's clear fake, but I kind of wish it wasn't
The problem is that the second you responded to something like that you'd be buried in copycats the next year all hoping to go viral. So you've made your job more difficult or burnt bridges on the way out the door.
The guy in charge of letting people in to one of the most prestigious universities in America is overworked? The hell you say! (That's supposed to be read as friendly, not actually incredulous)
For real, it's not like job applications where a lot of folks just cut the pile in half and toss them, then cut it in half again and toss them (yeah, I've seen managers do that for jobs with high application rates). They've got folks going through just checking that the admission was properly submitted, another layer making sure the people who properly submitted are qualified, then they're weighted to toss out any that fall below a certain percentage of qualification. Then the dean makes decisions. And they're still probably way overworked.
Something like this got tossed out by the lowest possible level and that person wouldn't even have the authority to write anything except a standard form letter that gets signed with an autopen.