no, no, and no
engine braking is not folklore. If you don't believe me, wait till a day where the streets are dry, and go to a flat level straight piece of preferably lightly trafficked highway. Get it up to 60, then coast to 20. Time yourself. Get it back up to 60, put it in neutral, then coast to 20. Time yourself. You'll slow down faster with the car in gear because the engine is braking the car.