WHILE DEVIATING AROUND SEVERE WX; ACR-LGT ENCOUNTERED ACR-WDB AT SAME ALT IN FOREIGN OCEANIC AIRSPACE; RESULTING IN LESS THAN STANDARD SEPARATION.

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APPROX 50 MI S OF PUERTO PLATA VOR WX DEVIATIONS WERE REQUIRED AND APPROVED. ACFT MAINTAINED FL290. AROUND 30 S OF PUERTO PLATA WE PASSED THE WX AND TURNED BACK ON COURSE. THE F/O NOTICED A WDB PASSING DIAGONALLY FROM RIGHT TO LEFT AT OUR ALT; XING IN FRONT OF US LESS THAN 2 MI DISTANT. ZMA WAS QUERIED AND SAID THEY HAD NO ONE BUT ACFT MIGHT BE WDB Y ASSIGNED FL280. THE CENTER THEN SAID THEY HAD THE ACFT READING AN ALT OF FL290. WE WERE STILL UNDER THE CTL OF SANTO DOMINGO BUT ALSO IN CONTACT WITH ZMA AS PER NOTE F ON LA HI/LO CHART 7--NOTE LOCATED JUST W OF PROVIDENCIALES. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: NO FOLLOW UP INQUIRY WAS MADE BY THIS FLT CREW. THE JUMPSEAT WAS OCCUPIED BY AN FAA INSPECTOR AND HE PROMISED TO MAKE AN INQUIRY AND LET THE FLT CREW KNOW EXACTLY WHAT CAUSED THIS INCIDENT. RPTR HAS NOT HEARD FROM THE FAA INSPECTOR AS YET. EVERYONE IN THE COCKPIT MADE THE ASSUMPTION THAT THE CENTER AT SANTO DOMINGO HAD ASSIGNED THE WDB FL290 AND HAD COORDINATED THE ACFT TO ZMA AT FL280. NO DOUBT THE DEVIATION AROUND SEVERE WX CAUSED THE ACFT TO BE CLOSER TOGETHER THAN THEIR ROUTES; W/O DEVIATION; WOULD HAVE ALLOWED. RPTR STATED THAT THE PROX OF ACFT WAS SUCH THAT THEY NEVER FELT IN DANGER AND HE EMPHASIZED THAT A NMAC DID NOT TAKE PLACE.