This was the controller's fault for the following reasons:
1.) The pilot initially stated he wanted 4L because of "landing performance." 4L at JFK has 11351 ft. available for landing whereas 4R has only 8400. Landing performance (i.e. braking distance) is highly correlated to the weight and type of the aircraft. The controller didn't seem to understand that for some strange reason.
2.) The pilot said they are "approaching the minimums for 4R." The pilot clearly meant minimums of braking/stopping performance. The controller mistook the word minimums to mean minimum decision height for for ILS in that 4R is a CAT-III ILS runway with "lower minimums" than the CAT-I ILS for 4L. But the pilot was not referring to ILS CAT scale minimums and was always referring to braking performance minimums with respect to stopping distance of available runway.
3.) The controller is a tool because he thinks he's lecturing the pilot on ILS minimums when it's clear to me he doesn't even understand the pilot. The fact that the pilot was from another country should have told the controller that there might be something lost in the language translation with respect to what the word minimums meant. The pilot was probably wondering why the controller is angry at him for simply wanting to safely stop his passenger jet on the longer runway with an extra 3,000 feet of stopping distance that was called for by the performance computer and mandatory to follow by Korean Air SOPs.
In fact, NTSB investigations have shown time and time again that Part 121 aircraft routinely violate company SOP's and FAR's when they land on shorter runways, especially when the runway is contaminated or there is a tailwind component.
4.) This isn't the first time we've seen this type of arrogance from JFK controllers. Avianca Flight 52 also comes to mind where the pilots declared "fuel priority" and the controllers instead put them back in the pattern and vectored them out over Cove Neck on a 20-mile final when they were on fumes. It should have been obvious to JFK controllers that you don't vector a jet out for a 20-mile approach when it's low on fuel and has made numerous references about its low fuel status prior to declaring a missed approach.
JFK controllers were in the wrong here 100%. Pilot was just doing his job. JFK controller was not.
Damn, I'm good. Smooth too.
So Mr. Smooth do you know whether the tower supervisor was standing behind the controller asking to find out the reason why KAL needed Ry 4L?
Are you aware that there is standard phraseology for low fuel situations? Trying to blame AVA on JFK tower is myopic. Why don't you read the NTSB reports that speaks to CRM in the cockpit. The Avianca disaster changed air traffic control in the US forever. It was that event that started the whole concept of ground delay holding to reduce excessive airborne inventory events.
Pilots who violate landing weight and balance rules are an accident waiting to happen. Airports are routinely in high crosswind and tailwind configurations because the USER'S want the increased efficiency at the expense of safety!

The rules of the game have changed in the last 10 years, atc no longer determines runway config's the airlines do. So please don't blame atc for high crosswinds and tailwinds!
Have you ever stepped foot into a busy ATC tower?