That they broke away from the English as their sovereign, conceded; that they broke away from the common law system itself, denied.
(Underline is emphasis mine.)
From United States v. Rhodes in 1866: "All persons born in the allegiance of the king are natural born subjects, and all persons born in the allegiance of the United States are natural born citizens. Birth and allegiance go together. Such is the rule of the common law, and it is the common law of this country, as well as of England."
From Ludlam v. Ludlam in 1863: "The same question is presented, therefore, in this respect, which arose in Lynch v. Clark (1 Sandf. Ch. R., 583), where it is, I think, very clearly shown that, in the absence of any statute, or any decisions of our own courts, State or National, on the subject, the question of citizenship can only be determined by reference to the English common law, which, at the time of the adoption of the Constitution of the United States, was, to a greater or less extent, recognized as the law of all the States by which that Constitution was adopted. This conclusion does not involve the question very earnestly debated soon after the organization of the government, whether the common law of England became the law of the Federal Government, on the adoption of the Constitution. (1 Tucker's Blackstone, appendix E, p. 378; 1 Story's Com. on the Const., § 158, and note 2; Madison's Rep. to the Virginia Legislature, 1799, 1800; Instructions of Virginia to her Senators in Congress, January, 1800; Speech of Mr. Bayard on the Judiciary, 2 Benton's Debates, 616; 1 Kent's Com., 331, 343.) It only assumes, what has always been conceded, that the common law may properly be resorted to in determining the meaning of the terms used in the Constitution, where that instrument itself does not define them. Judge Tucker, at the close of his essay against the common law powers of the Federal Government, says: "We may fairly infer, from all that has been said, that the common law of England stands precisely upon the same footing in the Federal Government and the courts of the United States, as such, as the civil and ecclesiastical laws stand upon in England, that is to say, its maxims and rules of proceeding are to be adhered to, whenever the written law is silent, in cases of similar or analogous nature.""
From Zephaniah Swift's 1795 treatise "A system of the laws of the state of Connecticut" (take note that Swift was member of CT's House of Representatives, a judge on the Supreme Court of CT from 1801 to 1819 [serving as Chief Justice for the last 13 years of his tenure], and ran a successful law school, among other things):
And so on.