I read both, and while they are interesting I believe that you are reading far to much into the directives and laws involved. Hair splitting.

“(c) An individual may not enter a sterile area or board an aircraft if the individual does not present a verifying identity document as defined in §1560.3 of this chapter, when requested for purposes of watch list matching under §1560.105(c), unless otherwise authorized by TSA on a case-by-case basis.”

It seems you are assuming that this says that you must provide that ID verifying document only to the aircraft operator. Not quite accurate, that is not what it says. TSA now does the watch list matching, so a request for the ID from a TSA employee is a valid request, if done so prior to entering the sterile area. The TSO will use that document to verify that the boarding bass or sterile area access pass is in the possession of the individual who’s name appears on the document. The TSO will also seek to verify that the ID document is valid, not a forgery, and actually belongs to the individual presenting it as ID.