Well, he's probably wrong. If someone is not eligible to the office, then they are not President. The Constitution says "The President, Vice President, and all civil Officers of the United States shall be removed from Office upon impeachment for and conviction of Treason, Bribery, or other High Crimes and misdemeanors". Nothing about ineligible usurpers.
That said, once a court determined that someone was ineligible, it may not be a Court that removes them. Might be, or it might be a "pitchforks and torches" delegation of the people.