That would be my intuition as well--especially for that route as traffic will frequently make driving pretty slow (and, indeed, that's sort of the point of the service).
It actually does, the problem is that the same restrictions do not apply.
A very large amount of private aircraft related accidents happen because of extreme conditions in which a commercial airliner would have not been flying under in any case.
Privately owned aircraft also tend to be much less well maintained and their pilots have considerably fewer flight hours than big or small commercial aircraft.
This is when "safety" takes a backseat to private ownership and responsibility, it's not because smaller aircraft are inherently less safe.
When embark on a private flight in a private aircraft there's virtually almost no circumstances in which you will not be cleared off for take off. Not to mention that anything upto a small jet can does take of from any sufficiently long patch of dirt rather than a fully staffed airport with ground crew that services and clears the aircraft.
If these guys will follow the same rules there is nothing much more inherently unsafe in being in a smaller or a rotary wing aircraft than in a brand new 747-800.
If you apply napkin calculations you can also make it sound that military aircraft are much more less safe than civilian ones, even in such cases in which they are the exact same aircraft in a different color scheme. It's not that the aircraft is less safe it's that the conditions it operates under are inherently more dangerous both in peace time and war.
First of all, you can't just mention a bunch of ways in which smaller aircraft are unsafe and then declare that they somehow don't count. If pilot experience and currency is a big factor for why small planes are more dangerous (and it most certainly is), then it's just a factor for why small planes are more dangerous, not some way that small planes aren't more dangerous.
For this specific service, there are a couple of things that do make it inherently less safe than being in a brand new 747-800. Specifically, there's much less redundancy and fewer emergency options for when something goes wrong. If you lose an engine on a 747 then you just keep going. If you lose an engine, or rather the engine, on a Manhattan-JFK helicopter flight then you're going down extremely fast and you have few or no good options for where to put the thing. It's similar for suddenly encountering a flock of geese (the odds of a safe landing in the river with a 100% survival rate are considerably lower with a helicopter than with an A320), fuel exhaustion, or a sudden pilot heart attack (I'm guessing there aren't two pilots in these things).
Mid-air collisions are another potential danger. I'm guessing that a helicopter like this doesn't have a TCAS system, and not all of the airspace in question requires ATC clearance. Nine people died in a helicopter/airplane collision in NYC in 2009, and it could happen again.
I don't mean to paint an excessively bleak picture here. I'd have no qualms about taking a flight on one of these helicopters, aside from the price. But at the same time we shouldn't kid ourselves by thinking that it's safer than taking a car, let alone as safe as an airliner.
If these helicopters are FAR Part 135 they'd likely have TCAS. Glass cockpit helicopters flown by commercial pilots are quite likely safer than driving.
Also, a skilled pilot can autorotate a Bell 407 without damage or injury. In fact, it would be easier than ditching a A320.
A friend of mine had a near mid-air in a Bell 407 over a city, flying between buildings, due to the other helicopter operating on an IFR clearance below authorized IFR altitude, shortly after takeoff. Luckily, this particular Bell 407 had EVS(Enhanced Vision System) FLIR (Forward Looking InfraRed) and they were able to descend hard and passed under "IFR" helicopter. The FAA busted the other pilot for failing to set their transponder correctly, and failing to maintain proper lookout, among other things.
Oh nice, I didn't realize TCAS was available there.
As for autorotation, my worry isn't so much the procedure (although it sounds much trickier than a gliding landing in an airplane) but the fact that you don't get much horizontal maneuvering and there aren't many good places to land in a dense city, and the fact that there are many single points of failure that make it much more likely to happen.
