A crew on a U.S. carrier would almost certainly have immediate access to cell phone communication while taxiing in to JFK from an international flight in my experience.
That doesn't mean that they should be required to use it though, especially considering that an unlisted phone number probably won't be recorded either.
The tower was probably just trying to be discreet by asking for a phone call. Unlike with the old analog AMPS system, modern digital cellphone transmissions are extremely hard to monitor without cooperation from the service provider from what I can see.
Agree with that, although they were probably only worried about the media getting their hands on a recording of the conversation and not about "terrorists hiding in the wheel wells with a gas mask" and possibly with a short-wave scanner too, for good measure.
The skipper's first responsibility is however towards his passengers and not towards ATC or Homeland Security or whomever was trying to avoid publicity.
Ciao,
Dg800