First of all, PHI has been teaching that "Cyclic Back" thing since the 1990s. In Recurrent Training the instructors taught us that our first response to an engine failure in cruise was to start the cyclic coming back...get the nose up...then lower the pitch.
And so I come down squarely with Pete Gilles and HeliComparitor on this. If the engine fails in cruise you must not merely - as Whirlybird huffily suggests - bring the cyclic back to just maintain attitude. Rather, you must get the nose up above the horizon to get the relative wind underneath.
If you're humping along at cruise and the engine quits, lowering the collective will introduce a strong nose-down tendency. The helicopter will immediately start to descend. Bringing the cyclic aft to maintain the cruise attitude will do nothing to correct this; you're still coming down. You have to bring the cyclic even further aft...get the nose up to get the rotor into autorotation. If you're flying a helicopter that cruises faster than it autos, why *not* take advantage of its ability to maintain altitude after the engine failure as you look for a place to land? Why not?
Now, if you're cruising along up at altitude it probably doesn't matter which you do first. If you push the collective down and see the RPM decreasing, your normal instinct will be to load the rotor with aft cyclic. Hey, you have time...what's the diff?
But what if you're dogging along down low...down at 500 feet, or lower, as many pilots do? You might not have an exact spot picked out for your auto (the auto that you're not really anticipating anyway). Trouble is, you neither have the time nor altitude to spare getting the thing set up for an auto. Every foot of altitude is precious. From 500 feet, lowering the collective without a corresponding large aft cyclic input is guaranteed to start an immediate descent. That could seriously limit your choice of landing zones, depending on the terrain.
I was puzzled at the infamous crash of that EMS ship in Missouri back in 2011. I was puzzled because the NTSB said it hit the ground so quickly after the engine quit. I think the NTSB figured that it was about nine seconds or thereabouts from engine failure to impact. And I thought, "How could that be? There's always time. Isn't there?"
I suspect that the pilot was probably frantic. He absolutely knew he was running out of fuel. His landing area (the airport) was in sight but the field boundary was still about a mile away. By this time he'd probably and involuntarily started a descent. So he was probably low...really low. He was screaming along, with the nose down and the rotor at a nose-low attitude toward the relative wind. Then it quit. His first response was to...to text his girlfriend that he'd be late for dinner...wait!...no!...no time for that!...just lower the collective!! Only that put him in an unexpected nose-down descent which was apparently not recoverable.
So Pete and HC, I'm with you guys. Stay the course! But I'll add that - from cruise now...if you don't want to descend - you not only have to make an aft cyclic input to *maintain* attitude, but get the cyclic further back and get the tip path plane tilted *up* and get some air underneath the disk.