[lepton]

The offense can not advance the ball by a fumble because we do not want to reward throwing the ball out of bounds. That makes sense. The offense can never earn yardage on a fumble (out of bounds).

Isn't that rule a response to the Raiders and their repeated forward fumbles in a playoff game? (Just an aside. I seem to recall that game.)

[SoothingDave]

Isn't that rule a response to the Raiders and their repeated forward fumbles in a playoff game?

Yes. They famously "fumbled" the ball forward to another player on a 4th and goal situation for a touchdown. So now, on any 4th down, and on every down in the final two minutes of a half, only the fumbling player on the offense can advance the fumble.