The Supreme Court has no such constitutional authority. It had such authority through arrogation by John Marshall in the case of Marbury vs. Madison in 1803, which is generally accepted but is certainly not overtly granted by the Constitution. If this is an example of the writer's understanding of the issue it calls into question the rest of his essay (I haven't had a chance to read it yet).
Yes, it does.
However true, therefore, it may be, that the judicial department is, in all questions submitted to it by the forms of the Constitution, to decide in the last resort, this resort must necessarily be deemed the last in relation to the authorities of the other departments of the government; not in relation to the rights of the parties to the constitutional compact, from which the judicial, as well as the other departments, hold their delegated trusts. On any other hypothesis, the delegation of judicial power would annul the authority delegating it; and the concurrence of this department with the others in usurped powers, might subvert forever, and beyond the possible reach of any rightful remedy, the very Constitution which all were instituted to preserve.
James Madison, Report on the Virginia Resolutions
The case of Marbury vs. Madison fell squarely within this authority since it was a case that concerned the executive and judicial branches of the general government.