From TSA Pre website, please explain why my take on this is wrong.
TSA Pre✓™ includes U.S. citizens who are members of existing Customs and Border Protection (CBP) Trusted Traveler programs including Global Entry, NEXUS, and SENTRI programs
as well as eligible airline frequent flyers.
more:
Certain frequent flyers from Delta Air Lines, American Airlines and
certain members of CBP's Trusted Traveler programs, including Global Entry, SENTRI, and NEXUS who are U.S. citizens are eligible to participate.
Interested passengers who are not eligible through their airline and are not already a member of a CBP Trusted Traveler program
may still be able to opt into TSA Pre✓™ by applying for one of CBP’s eligible programs. Click here to learn more:
http://www.globalentry.gov.
Airline Frequent Flyers
Alaska Airlines, American Airlines, Delta Air Lines, United Airlines and US Airways are contacting eligible frequent flyers with an invitation to opt-in. Once the passenger opts-in, the airline identifies the individual as a TSA Pre✓™ participant when submitting passenger reservation information to TSA’s Secure Flight system.
If a participating airlines’ frequent flyer did not receive an invitation from the airline, he/she can still participate by joining a CBP Trusted Traveler program. See below for more details.
Customs and Border Protection Trusted Travelers
Current members of CBP’s Global Entry, SENTRI and NEXUS Trusted Traveler programs are automatically eligible to participate in TSA Pre✓™.
Trusted Traveler participants will need to enter their CBP-assigned PASS ID number (located on the top right-hand corner of their Global Entry card) in the “Known Traveler Number’ field when booking travel reservations. Additionally, CBP Trusted Traveler participants can add their PASS ID number to their AAdvantage® or Delta
This link takes you to a nongovernment website that may have a different privacy policy.member profile to have the number automatically sent to TSA when booking reservations.
Note: It is not necessary for CBP participants to opt-in through both CBP and a participating airline.
Members are automatically eligible to participate by virtue of their enrollment in the CBP qualifying program.