crab and Wageslave~
The nature of their police work often means low and slow, an awful place to be over congested areas. As I live but a mile from the helipad, I often see them flying nearby, and say a quiet prayer for a safe flight. When I could afford to regularly fly helicopters (I'm a PPL and would rent), I flew a little higher, and was looking for a landing spot as much as for other air traffic, especially as I was flying the low-inertia R22. I think this police flight ended well due to the great emphasis they put on practicing autos, and therefore muscle-memory. Did good luck help? Maybe, but hard to quantify. On modern single-engine machines, whether turbine or piston, power loss is uncommon. Of course, if it's one-in-a-million, and you pull the one straw, the odds are meaningless. I don't know one could say that training can compensate for lacking a second donk, but being prepared and expectant could only help, regardless if you're driving a helicopter or locomotive.
chopjock~
I do remember my CFI friend saying that the throttle was checked open. I don't know about the pump, I'll see if I can find out.