That is pretty funny. You use an old version of a regulation that was revised in 2008 and then when I point that out to you, you claim I "missed" a section, which you didn't even know existed since it didn't in the old regulation you first quoted. That is the thanks I get for helping you in your research?
Be that as it may, did you decide not to look at §1560.105(c) or did you do so and not like what you saw since it doesn't support your view? Let's look at those C.F.R.'s:
1540.107(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.
So what does 1560.105(c) say:
Request for identification (1) In general . If TSA has not informed the covered aircraft operator of the results of watch list matching for an individual by the time the individual attempts to check in, or informs the covered aircraft operator that an individual has been placed in inhibited status, the aircraft operator must request from the individual a verifying identity document pursuant to procedures in its security program., as provided in 49 CFR part 1544, subpart B or 49 CFR part 1546, subpart B. The individual must present a verifying identity document to the covered aircraft operator at the airport.
So it is the airline that has to ask for the ID, and only under specified circumstances. What happens if the airline fails to obtain that identification:
(d) Failure to obtain identification . If a passenger or non-traveling individual does not present a verifying identity document when requested by the covered aircraft operator, in order to comply with paragraph (c) of this section, the covered aircraft operator must not issue a boarding pass or give authorization to enter a sterile area to that individual and must not allow that individual to board an aircraft or enter a sterile area, unless otherwise authorized by TSA.
I think that there is a reason why the TSA is not involved in this process directly with the passenger.
So once again, how does that in the least govern the presentation of id at the checkpoint?
"Good enough?" No. It does not appear that you "can read it and understand what [you] read."