A DEPARTING ACR B767 IS RESTR TO 4000 FT DUE TO VFR CLASS B TFC AT 4500 FT. TFC WAS ISSUED BY THE CTLR AND THE B767 CROSSED BELOW THE VFR ACFT. THE B767 PLT MENTIONED THAT THEY HAD RECEIVED A TCASII RA TO CLB; BUT REMAINED AT 4000 FT. THE CTLR CLAIMS THAT THE PLT'S ACTION TO REMAIN AT 4000 FT PREVENTED A MISHAP.

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WHILE WORKING KENNEDY DEP RADAR IN NOV 1996; AT XX00L A VFR ACFT SMA Y; A PA28A WITH OPERATING MODE C; WAS CLRED THROUGH THE KENNEDY CLASS B AIRSPACE SWBOUND AT 4500 FT. ACR X; A H-B767 WITH TCASII DEPARTED RWY 31L AT JFK AND WAS RESTR TO 4000 FT. ACR X WAS LEVEL AT 4000 FT AND TURNED NEBOUND. TFC WAS EXCHANGED BTWN ACR X AND SMA Y. THE 2 RADAR TARGETS MERGED AND WHEN THEY SEPARATED I ISSUED A CLB TO ACR X. A FEW MINS; AND ABOUT 20 MI; LATER ACR X ASKED ME IF THE VFR THAT HE HAD CROSSED HAD OPERATING MODE C. I REPLIED AFFIRMATIVE AND ACR X REPLIED THAT HE HAD RECEIVED A TCASII RA WHICH HAD TOLD HIM TO CLB. I VERIFIED THAT THIS IS WHAT HE WAS INSTRUCTED TO DO AND HE CONFIRMED THAT THE RA WAS TO CLB. I TOLD HIM THAT I WAS GLAD HE DID NOT FOLLOW THE RA AND THAT HE SHOULD RPT THE EQUIP TO HIS COMPANY. THE B767 CROSSED DIRECTLY BENEATH THE VFR PA28 WITH APPROPRIATE SEPARATION. A CLB BY THE B767 AT THIS TIME COULD HAVE BEEN DISASTROUS. THE ACR X PLT WAS OUT OVER THE OCEAN AT NIGHT WITH NO HORIZON TO HELP HIM JUDGE THE ALT OF THE VFR ACFT. ONLY HIS FAITH IN THE TFC CALL I HAD ISSUED PREVENTED A MISHAP. THIS IS NOT THE FIRST TIME I HAVE HEARD OF TCASII ISSUING ERRONEOUS RA'S BUT THIS IS ONE CASE WHERE IT COULD HAVE BEEN FATAL.