This requirement is ONLY for US registered aircraft. Aircraft coming from foreign countries are exempt. ALSO aircraft from foreign countries cannot go from one domestic stop to another. Where ever they land, their departure MUST be back to foreign soil.

Example: A British Airways jet lands in New York, it cannot fly on to Chicago from New York. Passengers must go by a US carrier from New York to the Chicago destination. It is usually the same in other countries for US airplanes.