This situation definitely would have turned out very badly, due to the high density of population and buildings, etc. in the area, if they had been a little lower or "dirtier" when the damage occurred... although in that case, "Sully" would probably have tried to ditch in the water immediately surrounding the airport (the upper reaches of the East River, where it connects to Long Island Sound).
And if they had continued to try to make two left turns to land on 04 at KLGA, it probably wouldn't have worked.
But it's not like the controller was making rash assumptions- he was only trying to assist the PIC of the flight- who has the final say in any case.
If you examine the transcript closely, you see that the Capt. was the first to come up with the idea of returning to KLGA... so, despite being told they'd lost thrust in both engines, the controller, figuring they knew better then he did what was possible at that moment, gave them a heading to set them up for an emergency approach for Runway 04 (which they had just taken off from).
But less than a minute later, the Capt. informed him that it would probably not work... he was already considering the river (that's a glider pilot for you...

).
Still less than two minutes after the strike, while basically lining up for the river, he considered KTEB, but quickly forgot that idea, realizing the angles wouldn't work. Good thing, too... at that point, they were only at about 2000 MSL, about 5 miles from KTEB. they would have had to glide all that way, then turn to line up with Runway 01 there. No way that was going to happen. KTEB is a big airport, but it's surrounded on all sides by development and roadways. Not as bad as NYC, but had they panicked and tried to make KTEB, it would have been disastrous.
So he continued with the ditching approach. Interestingly, the
cockpit transcript shows that while doing all this, he had the FO trying to coax some life out of one of the engines, which briefly looked as if they might re-light. Good use of cockpit resource management... and worth a try, even though they knew it would probably not work.
This transcript includes cockpit and ATC comms... interesting reading. What's amazing is how little time actually elapses from bird strike to "splashdown"... crew and ATC were a little freaked-out (controller started calling them by the wrong flight number, Sully started thinking about KTEB), but everyone did their jobs properly... Sully made the right choice, and the controller shifted gears quickly enough- did his best to alert authorities near the river, and even enlisted the aid of other flights over the river to get a situation update.
http://www.usatoday.com/news/nation/2009-06-09-hudson-cockpit-transcript_N.htm