Two reasons he can do it:
1. There is no Supreme Court precedent that interprets the Constitution differently.
2. The Constitution does not explicitly say that the Supreme Court's interpretation of the Constitution generally overrides that of either Congress or of the President, who are co-equal branches of government. The Constitution does explicitly grant the "Judicial Power of the United States" to the Supreme Court, but nowhere is that defined as the ability to set binding precedents that the other two branches must respect beyond the parties to the cases for which the Court has issued a ruling. At most, it requires that the other two branches respect the Court's decision as it applies to the parties to the cases brought to the Court, but not that they do so for other parties who haven't petitioned the Court, and whose cases the Court has not adjudicated. In other words, if Jose Illegalson sues to be granted citizenship under the 14th Amendment, and the SCOTUS rules in his favor, the Executive Branch is only Constitutionally required to treat Jose himself as a citizen, not his sister Manuela, who didn't petition the Court, and so who has no SCOTUS ruling that personally applies to her.
Nowhere does the Constitution incorporate English Common Law into US Law, neither with respect to any precedents set by British courts, nor with respect to principles such as "stare decisis." Several prominent Founders argued exactly that, including Madison and Jefferson.
IOW, the courts are not the final arbiter of what’s constitutional. If they were, then we’d have a judicial tyranny. Oh wait, that’s what we have now.