Well they are determining the "Airworthiness" of the aircraft. What paperwork is required to be on board for the aircraft to be "Airworthy"
§ 91.203 Civil aircraft: Certifications required.
(a) Except as provided in §91.715, no person may operate a civil aircraft unless it has within it the following:
(2) An effective U.S. registration certificate issued to its owner or, for operation within the United States, the second duplicate copy (pink) of the Aircraft Registration Application as provided for in §47.31(b), or a registration certificate issued under the laws of a foreign country.
So unless you are voided by 91.715 then you are required to have a registration certificate.
Or atleast that is my opinion