You misunderstood. Of course the GAs don't validate pax against the no fly list. This is done in the background.

But if your name is JOE and you are on the non-fly list, you won't be able to check-in for a flight as JOE. So you go ahead and book a ticket in the name of JIM. Then you show up at the boarding gate, and unless the GA validates that your ID says you are JIM, you have just boarded a plane when you shouldn't have. (same story for reselling flights: JOE bought a non changeable ticket but can't make it, however his buddy JIM can...)