He's right. The original intent of the Constitution was that it was a treaty drawn up under the Law of Nature and Nations by Vattel, who repeated the words of a great many philosophers like Aquinas.
Taking all that into consideration, a more accurate beginning would have been:
The People, through their Representatives of the American States.
But the Founders shouldn't be faulted for it. I don't imagine they EVER thought the People would forget that they are inherently superior to government.
The purpose of the Federal Convention was to frame a government sufficient to the objects of a free people. The Constitution is not a treaty or series of treaties, as the Articles of Confederation were. Vattel was one of several philosophers reference by the Framers; Locke and Montesquieu were the most notable as demonstrated by the government they proposed.
The elements of good government were already known to the Framers of 1787; no deep philosophical debate as to what constituted good government was necessary. States had over twenty years since the Stamp Act to think about the successes and failures of their various State constitutions. Convention delegates had plenty of practical experience and put them to paper, despite lingering deep suspicions and factions.
The People, through their Representatives of the American States.
Not accurate. The States held special elections for delegates to the ratifying conventions. To say representatives of the states is to mean the States in their corporate capacities, i.e. legislatures.
I don't imagine they EVER thought the People would forget that they are inherently superior to government.
Quite right, and certainly not to extent we have.