Well isn't this an interesting discussion...
OK, I've checked my FOM for the 757/762/763 and the max crosswind speeds are 30/29/33kts respectively with a max tailwind of 10kts for all a/c. If the winds were 320/23G35, that would have exceeded the aircraft's max crosswind/tailwind component. The pilot would have needed 31R, but what is unclear to me is why the pilot felt he needed to threaten the controller with an emergency if he didn't get 31R? From the ATC tapes I've heard, we don't know if there was previous discussion between AA2 and ZNY approach or the tower about the winds and conditions for 22L or if there was a fuel emergency involved. If there was a potential fuel emergency involved and it was impossible for the aircraft to make an extended orbit, then it would have been useful for the pilot to explain that from the start.
However, once the pilot declared an emergency, for whatever reason, he should have been immediately been given immediate priority for 31R. Things got ugly between the pilot and the controller when the controller didn't immediately give AA2 the left turn. The pilot then informed the tower of his intentions (correctly so) and once this was clear to everyone, the controller cleared him for immediate landing on 31R. Once that exchange was complete, the controller was clearly scrambling to get traffic out of the way.
This is a tough call...I believe in this particular situation, there should have been traffic directed to land on 31R or 22L and in situations in which a landing would have exceeded the crosswind limit, the pilot should indicate his intention to go around and request 31R (and get it) based on his judgment of the conditions. While I recognize this would have created a mess at the airport, better that than a situation in which a pilot declares an emergency simply to get the runway he needs to safely land the aircraft.
BTW, in the USA, I do not believe is not necessary for pilots to declare a mayday to declare an emergency.
AFAIK,they only need to state that they are declaring an emergency and that places ATC on notice that an emergency exists and that they must act accordingly. We had an incident at KSEA last year in which an Asiana 777 lost an engine on takeoff and only "declared an emergency" as the aircraft was able to fly on one engine and return (three hrs later after dumping fuel).
If a pilot declares a mayday during an emergency - in US airspace, then the aircraft is in an extremely dire situation.
Dave Lamb/speedbird716