The reason “law school types” make that argument is that law school curricula feature only lots of case law and, occasionally, a few excerpts from THE FEDERALIST. Since that’s all “law school types” know, they have a vested interest in saying that’s all that matters.
On the other hand, their assertion is nonsense: the Philadelphia Convention merely wrote a proposal. As Article VII says, it had no effect until ratified by 9 states, and then only in the states that had ratified. As Madison said in THE FEDERALIST and Jefferson said elsewhere, it was to the ratification conventions that one must look for the Constitution’s meaning. Why? Because it was the explanation(s) the Federalists gave during the ratifcation conventions that the people ratified.
Popular government — government by the consent of the governed — is the government to which the people consented, not some gnostic secret cult’s private reading. The latter sounds very Straussian.
Ask your “law school type” friends this question: what if the Philadelphia Convention had secretly agreed that members of the Philadelphia Convention would be our king and lords, or that they had envisioned a military dictatorship, along with abolition of press freedom and trial by jury, would that then be what the Constitution required? Please.