I recall seeing somewhere that an airplane is a machine that wants to fly, the engine and controls just help it along. A helicopter is a machine that desperately wants to crash, the engine and controls constantly fight against this.

A helicopter that loses power at altitude can often still land safely due to autorotation. I am no pilot but I've read that the JetRanger is particularly competent in this flight envelope. See http://en.wikipedia.org/wiki/Autorotation and http://en.wikipedia.org/wiki/Height-velocity_diagram for more info.

On the other hand, losing the tail rotor is always Very Bad and quite difficult to survive. It's possible that this is what happened in NYC.

You are probably thinking of Harry Reasoner's quote:

"The thing is, helicopters are different from planes. An airplane by its nature wants to fly, and if not interfered with too strongly by unusual events or by a deliberately incompetent pilot, it will fly. A helicopter does not want to fly. It is maintained in the air by a variety of forces and controls working in opposition to each other, and if there is any disturbance in this delicate balance the helicopter stops flying; immediately and disastrously. There is no such thing as a gliding helicopter.

This is why being a helicopter pilot is so different from being an airplane pilot, and why in generality, airplane pilots are open, clear-eyed, buoyant extroverts and helicopter pilots are brooding introspective anticipators of trouble. They know if something bad has not happened it is about to."
-Harry Reasoner

(I got the quote from http://www.ga-vhpa.org/musings.html, and also Tim Setnicka quoted part of it in his book 'Wilderness Search and Rescue')

In a hypothetical situation with loss of engine power, although it might be possible for a falling helicopter to flip over due to wind shear or some other violent turbulence, I don't recall ever hearing of a helicopter flip over like that. Since the engines are quite heavy and autorotation (even upside down) tends to create drag from the rotors, I think the tendency of an upside down falling helicopter would be to flip back over, rightside up again assuming there was enough altitude and time.

But that's different from the hypothetical I mentioned, where the rotor strikes something that physically stops the rotor so that the momentum and torque present in the rotor suddenly needs to find something else to turn, namely the rest of the helicopter.

Once in the water, however, the dynamics totally change. The body of the aircraft then becomes a top heavy floating object and the weight of the engine and main rotors will want to go to the bottom, the same way that a car in the water typically sinks nose first. It's kind of like trying to lie on top of a big beach ball in the water--the tendency is for the heavy object, i.e. you, to go under while the buoyant ball is pushed upwards by the water.

I've always been amazed that people continued to try and develop the helicopter until they got it to work. Unlike the way a fixed wing aircraft works, a helicopter is just brute force exerted against gravity in a battle to stay aloft. Then again, we do have hummingbirds and other hovering birds in Nature, too.