The article posted earlier about Wall:

says that he is still a walk on and mentions an academic scholarship, so I think you are correct.
The article also has this bit:
Wall, who is now a redshirt junior in his fourth year in the program, had a football scholarship offer from William & Mary University, a full-ride academic scholarship at Virginia, and was given the chance to be a preferred walk-on at Virginia, where former BYU coach Bronco Mendenhall was the head guy. He was also recruited by Ivy League schools Columbia, Harvard, Princeton and Yale.

indicating he had the chance to go UVA academically and walk on with them like he has here.