Yes--the airline's website is irrelevant--the fare inventory and the booking system is what counts. We don't book through the airline, we "are" the airline as we hook directly into their systems.

AA.com for example is basically a graphical, consumer-friendly interface for Sabre, their back-end system that manages flight inventory & operations. Any AA gate agent, Admiral's Club staff, check-in agent, etc operates in Sabre. (Post-merger they use graphical overlays integrated in the proprietary Sabre interface that limit what they can do (i.e. overriding fees, upgrading, etc))

This is my whole point. Whether it's the airline website, an OTA, or a phone call with me, we can all see the same pricing & availability when it comes to published airfare rates. Expedia and OTAs just choose to put distractions like "ONLY THREE SEATS LEFT", timers, etc to create time urgency, which is one of the oldest marketing tactics in the book to close a sale. It's effective, certainly, but not usually accurate.