agree with rananim and mountainbear in almost all aspects, but the AF skipper is not to blame - it's all ATC fault - maybe a little too relaxed. Or was the skipper given Taxi clearance on "own discretion" ? - for shure not.
On a good airport with good controllers all my career long we were always advised to stop, or to hold short or.... until the ground traffic was clear. sometimes the controllers were overcautious and also we reported clear from ground traffic they were waiting for info from additional sources. so JFK obviously a "special airport" with "special"
ground controllers...