First of all, the ATC tower has NOTHING to do with this. The GA agent may have been referring to the local DL operations "tower" that controls things on the ramp. In all liklihood, that gate was about to be needed for an arrival that was already on the ground and taxiing in. The gate situation at JFK gets very tight from about 1PM onward. However, that said, I also would have been PO'd.

Contrast this to what happened to my wife and I a couple of years ago when travelling to Scotland on CO... typical BOS-EWR delays for summer thunderstorms... flight arrived at 830PM, the exact time of our GLA flight departure. We hear our names being paged overhead in the terminal as we left the first flight, charge through the terminal (felt like tossing my cookies!) and arrived at our GLA gate. Only after we were seated in our BF seats did we learn that the doors had actually been closed, escape slides armed etc., when the call came to disarm the doors and open the boarding door back up.
Even more amazing, our luggage made the connection.

And at CVG, we have had our PDX flight held at the gate when we were late arriving into CVG.

The decision whether to hold a flight for inbound connections is complex and has been discuissed on the board many times. Is the gate about to be needed for an inbound aircraft? Is there a later flight to accomodate the potential mis-connects or will they be stranded overnight? Will the departing aircraft be overnighting at its eventual destination or will it be immediately turned for another flight? Are there crew rest issues and duty time issues that come into play with a delay?