I'm not surprised that a flock of geese could take out both engines. While a single "V" in flight doesn't look that big, sometime the traffic density is - higher.
Birds Ascending the Heights
In terms of landing on the river, my point was precisely that: with a 20 mile x 3000 ft "runway", there is no need to stretch the glide. Come up a couple of hundred feet short, and you still have open water surface.
Come up a couple of hundred feet short at Teterboro, and you may have a burning plane and crushed buildings.
In the middle of a huge populated area, the water was the best "bailout" option. (Pun purely incidental).