Why was this helicopter denied entry to Class B airspace?
According to the post at LiveATC, Newark was closed, apparently due to smoke in the tower. With the airport closed, nobody could be granted clearance to take off or land. 

Outside of declaring an emergency, there's nothing the pilot(s) could have done to get clearance at Newark other than just waiting. 

In an emergency situation like smoke in the tower, there wouldn't be anything published beforehand for the pilots to look up, but otherwise, pilots look at NOTAMS during their flight planning for planned closures or outages. Even in good weather, proper flight planning would also involve an alternate airport, anticipating the possibility that the intended airport might be closed for an emergency like this.

Eight miles south of Newark is Linden Airport, a small uncontrolled field just outside the Class B surface area. If I had passengers in my ship who were trying to fly out of Newark, I would have radioed operations and asked them to send a limo to Linden to pick up my passengers.



[There is one part of the recording that says "[inaudible]". The pilot is announcing his position at the Statue of Liberty, a reporting point for copters landing EWR.]