They can be refuted directly by one of the founding fathers, Benjamin Franklin.
There is no doubt that the Founding Fathers did not exclusively use the English translation, but relied upon the French original. On December 9th of 1775, Franklin wrote to Vattel’s editor, C.G.F. Dumas:
“ I am much obliged by the kind present you have made us of your edition of Vattel. It came to us in good season, when the circumstances of a rising state make it necessary frequently to consult the Law of Nations. Accordingly, that copy which I kept has been continually in the hands of the members of our congress, now sitting, who are much pleased with your notes and preface, and have entertained a high and just esteem for their author.”
They are saying..the 1760 book is in French..and the Founders were English and could not read it. They say the 1760 edition does not have the words natural born citizen. The words were added in an later English edition after the constitution was ratified.
I found Jefferson read Montesquieu’s Esprit des Lois. He copied into his notebook (in French) numerous quotations.