A fair catch must be executed in or beyond the neutral zone (6-5-2). K can catch or recover kicks beyond the neutral zone if they were first touched by an R player (6-2-4). I agree that K can advance on a kick caught or recovered in or behind the neutral zone.
However, if R makes a fair catch signal in the neutral zone, R must be afforded an unimpeded opportunity to make the catch. This constrains K's ability to catch and advance the scrimmage kick in the neutral zone.
In most scenarios, the fair catch will happen beyond the neutral zone, so it is rare that a back judge will have to rule on fair catches in the neutral zone. In that case, it will be the short wing who has to decide on that play.
Just to play devil's advocate (not HFHS so I don't know the exact verbiage or details of that rulebook):
4/10 @A40.On a scrimmage kick, K86 shanks the ball high and short and straight ahead. R45 signals for fair catch 10 yards downfield while running up to field the ball, and is positioned to catch the ball 3 yards behind the NZ at the A37. Big 'ol Bubba K76 impedes R45's attempt to catch the ball by knocking him to the ground while he is trying to make the catch, and makes obvious, intentional contact with the ball. K32 recovers the kick at the A35 and advances the ball to the EZ.
Ruling?