As one who has spent a fair portion of my life at JFK I just cant belive that anyone would expect the Ground Controllers to warn crews about every potential collision posibility, {they cant even see some gates} dear God they would never stop talking or come up for air! Its real simple, the buck stops in the left seat, period!
I'm not sure what the FAA's take is, but under ICAO preventing planes from hitting one another on the ground is a controller's second overarching responsibility (after stopping them from doing so mid-air). It may not be practical to do so verbally at JFK, but procedures (especially for 380's) & aerodrome design should contribute to making it possible for them to effectively prevent collisions. If it's not their job they just become "Ground Movement Enablers" or some other HR concoction. Yes the AF crew failed to operate the aircraft safely, but the buck certainly does not stop there.