The LGA departure controller can suggest almost anything. However, in an emergency such as this its the responsibility of the PIC (Sully in this case) to make the decision based on circumstances and information at hand.

It might have changed things if LGA departure had immediately mentioned all possible airports in the vicinity. However, as has been mentioned, TEB presented risks of its own. The surrounding buildings, 7000 foot runway (probably OK, but who knows what the state of the hydraulics were given the use of the RAT), and likely downwind landing on runway 19 would have made things very risky.

Note that LGA departure didn't suggest JFK to Sully. It was farther away, but does have longer runways than TEB). Also, they mentioned EWR, again with longer runways but at a greater distance. IMHO (and it is only my opinion...) Sully made the right call and the controllers did what was required.