I am familiar with this location. The Department of Education is a very large building. The main entrance is on Maryland Avenue, whereupon visitors must pass through security, sign in and get a visitors pass. The doors in the video are on C Street, on the rear side on the building.
An "All Access" entrance is what used to be called a "Handicapped Entrance" until the word handicapped fell out of favor and the signage was changed. This would be an additional access point for those with special needs, particularly at older or historical buildings where the main entrance can't be retrofitted to comply with ADA. These locations are often unstaffed and locked, with an intercom to request access.
The Members choice to tug on the doors of a handicapped entrance, en masse, rather than go to the main entrance (generally unlocked, but with a lobby and security checkpoint) seems a bit theatrical and detracts from their message.
That might be common sense, but that airport is too crowded to provide that much leeway. It is to busy, too many physical obstructions, and to many restrictions that funnel traffic into confined pathways. . There has been a push to close it for decades, exacercerbated by the Air Florida crash. Meembers of Congress (who enjoy the conveninece) overuled that. I recall when, for a time, airlines were prohbited from scheduling connecting flights via National, or use it as a hub. Congress didnt like that either, because less flights coming through meant less flexibility for their schedules. My family members won't fly into or out of that airport. Too scary.