When you are graded on every play, you need to cover your bases. The hat shows that you saw your key go OOB's one way or another, and then a flag if needed for ILT or a team A player going OOB's on his own and returning IB's during the down.
Being my own advocate .... why do we have to cover our arses in this situation, but not in others with similar basic dichotomy.
Examples
1. From chymechowder: Prior to the snap, the L notices that TE (A87) is covered up by the wide receiver. At the snap, A87 goes downfield and runs his pass pattern. A87 has committed a foul if the QB subsequently throws a pass that goes beyond the neutral zone. No pass beyond the NZ; no foul. We don't toss a hat when A87 goes into pass pattern.
2. From scrimmage kick formation, a punt protector (A55) blocks rushing B45 below the waist. The punter catches the snap and runs outside the tackle box looking like he may kick the ball a la soccer style. A55 commits a foul if the punter kicks the ball. However, if the punter tries to run for a first down, there will be no foul. Again, we don't toss a hat when A55 blocks below the waist.
Where's Elvis; we need Elvis. He always had answers for these sorts of discrepancies.