If the argument doesn't fly, it's not for that reason. Article 2, Section 1, Clause 5, of the Constitution allows for "a Citizen of the United States, at the time of the Adoption of this Constitution" to run for president, and that grandfather clause qualified the first twelve presidents.

I'm not sure if the corporation that is Harvard is the same entity that was Harvard around 1787. I doubt it was considered a citizen of Massachusetts at the time, but that may not have any bearing on a modern legal viewpoint is that Harvard truly was a citizen then.