putting the automatic transmission in neutral with the engine running disengages the geartrain, like depressing the clutch pedal on a manual transmission. - note that with modern automatic transmissions, the engine must be running to keep the transmission fluid circulating; which lubricates the geartrain.
however, my state and probably many others, prohibit the practice of coasting down hills with the transmission in neutral. the logic behind this is that first, the engine helps with braking on downgrades, and reduces heat and wear in the brakes - critical in heavy vehicles. second, if the transmission is disengaged, then the transmission will have to be reengaged before the driver can accelerate to avoid trouble.
1) it is illegal in most states
2) It takes some control away from the car, especially when you're on a surface that is not dry
3) It's possible to forget you're in nuetral and either slide it into park or race the engine thinking you're in drive
4) the engine braking effect actually helps you maintain control and have less wear and tear on the brakes
5) you have no control over the car in an emergency
6) the car is still turning over at idle, and coming down the hill with your transmission engaged, the car is still in idle - you're not saving as much as you think
7) the rear seal of the transmission is not being properly lubricated when you're in idle and the drive shaft is engaged. This is one of the reasons a rear wheel drive vehicle should not be towed great distances.
All in all, your friend is correct. Just let the engine idle as you come to a traffic control device that requires you to stop.