The likes of Expedia don't deliver a lot of good premium traffic; the bulk of this comes from corporate agreements, travel agents (still), and the airline's own website. Most of what Expedia can deliver is bottom-priced stuff. It's not inconsequential, but it's also what airlines can most easily get out of.
American have lost some headway in the "general" US market in recent years, but are still ahead in good, big corporate agreements. One of the few things that came good for them from the TWA acquisition was the marketing agreements with the media business in New York and Los Angeles which lingered with TWA from their former great years, which is part of why AA still dominate this particular city pair, and why you will still find more media personalities on board an AA flight than any other. You'll find the same with the heavy business traffic between Miami and Latin America. The bottom-price trade down here is on board the local South American carriers.
Different focus.