Knowing what I know about TV production, he may have played the guitar part ahead of time to record it separately, then "lip synched" while actually filming. But yes, his movements and chord changes looked very natural and authentic. You don't want a minor playing mistake to cause another whole take of the scene.
I don't fully get why they covered the head stock logo, but at least they used a colorful little design. Normally they just use a big blob of black gaffer's tape.