I agree that some teachers have taken this concept too far, but it's a darn good idea for three things:
1. Practicing on surfaces with little rebound (technically, even the floppiest pillows have SOME rebound) helps you learn how to work with little rebound...thus building your muscles, much like lifting weights, or a baseball player swinging two bats (or a weighted bat) before going up to hit. They never actually hit with two bats, but they use them to build those muscles, and warm them up.
2. Using rebound in drumming involves a lot more than just the rebound...it involves controling the minute muscles in your hands, wrists, and fingers. By using a surface with less rebound, you really learn how those muscles work, and what you have to do to control them totally and well. I have gained a great understanding of how your hands can manipulate a drum stick by playing on surfaces with little rebound.
3. Frankly, a lot of students don't put in nearly enough time drumming, in large part because they don't want to just focus on drumming (as opposed to TV, etc), and in large part because family members complain about the noise, even on a pad. By telling your student to practice on a pillow, you gain the two advantages I mentioned earlier, and also the ability to have them practice silently, and practice while watching TV, listening to music, talking on the phone, etc.
It is a great thing to do that many professional drummers have done throughout the years, but it doesn't replace playing on a drum. Something like a Real Feel pad, well, they are usually more bouncy than a normal drum, so that can actually be detrimental...you can play stuff on there that you can't play on a drum, and really, it only matters what you can do on the drum.