A300 CREW INBOUND TO CCS (VENEZUELA) AT FL330 OBSERVED A B767 DSND THROUGH THEIR ALT APPROX 2-3 MI AWAY; VISUAL AND TCASII DISTANCE. THE CREW CLAIMS THAT THE CTLR INSISTED SEVERAL TIMES THAT THE TFC WAS 10 MI AWAY. THE FLT HAD BEEN ON CURACAO CTL AND WERE IDENTED BY MAIQUETIA CTL AND IDENTED AT REPIS INTXN 32 MI SE OF PJG VOR (A COMPULSORY RPTING POINT).

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ENRTE FROM MIA TO CCS AT REPIS INTXN WE CHKED IN WITH MAIQUETIA CTL; RPTING TIME AND ALT. MAIQUETIA RPTED THAT WE WERE RADAR CONTACT AT REPIS. AT THIS TIME MY FO POINTED OUT AN ACFT DSNDING THROUGH OUR ALT IN CLOSE PROX. WHILE THERE WAS NO IMMEDIATE THREAT OF A COLLISION THIS WAS NEVERTHELESS VERY ALARMING. I SCALED DOWN THE TCASII TO THE 5 MI RANGE. THE TARGET WAS JUST 2 1/2 MI AWAY AT THE 11:30 POS. AT THIS TIME MAIQUETIA CTL INFORMED US OF AN ACR Y B767 ACFT THAT WAS DSNDING TO FLXXX AT OUR 10 O'CLOCK POS AND 10 MI. WE INFORMED MAIQUETIA THAT THE ACFT WAS NOT 10 MI OUT; BUT INDEED 2 OR 3 MI IN FRONT OF US DSNDING RIGHT THROUGH OUR ALT. MAIQUETIA INSISTED THAT THE ACFT WAS 10 MI IN FRONT OF US. THE TCASII STILL SHOWED THE ACFT AT THE 2-3 MI RANGE DSNDING. VISUALLY IT WAS OBVIOUS THAT THE ACFT WAS INDEED WITHIN 3 MI. WE SCANNED THROUGH THE RANGES TO DETERMINE IF THERE WAS MORE THAN 1 ACFT INVOLVED -- THERE WAS NOT. MAIQUETIA CONTINUED TO INSIST THAT ACR Y WAS 10 MI IN FRONT OF OUR ACFT EVEN AFTER WE OVERTOOK THE B767. MOREOVER; MAIQUETIA WAS BASING THIS NOT ON POS RPTS; BUT ON RADAR INFO. THIS INCIDENT CAME WITHIN 2 MI OF A MIDAIR COLLISION. ACR Y COULD EASILY HAVE DSNDED RIGHT ON TOP OF US ON THE ASSUMPTION THAT MAIQUETIA WAS PROVIDING PROPER RADAR SEPARATION. CLRLY THERE IS EITHER SEVERE SYS OR OPERATOR ERROR INVOLVED HERE. THIS NEEDS TO BE ADDRESSED ASAP. AS A FOOTNOTE; WE SPECULATED THAT CURACAO CTL MAY HAVE WANTED A POS RPT FROM US AT PJG. AT NO TIME DID EITHER MY FO OR MYSELF UNDERSTAND THAT CURACAO REQUESTED THIS AND WE PASSED BY PJG WITHOUT A RPT. WHETHER THIS HAD ANYTHING TO DO WITH MAIQUETIA CTL DSNDING AN ACFT RIGHT THROUGH OUR ALT WITHIN 3 MI OF US IS UNKNOWN. IN ANY RESPECT; THE SYS FAILURE OR OPERATOR ERROR THAT ALLOWED THIS TO HAPPEN MUST BE ADDRESSED AND CORRECTED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT THEIR FLT WAS ON FREQ WITH CURACAO CTL; NON RADAR; UNTIL THEY WERE OVER REPIS THEN SWITCHED OVER TO MAIQUETIA CTL. OVER REPIS; THE FLT WAS RADAR IDENTED BY MAIQUETIA CTL. PJG VOR IS 32 MI N OF REPIS AND IS A COMPULSORY RPTING POINT. THE RPTR WAS ASKED IF THEY HAD RPTED OVER PJG AND THE RPTR SAID NO. HE STATED THAT MOST OF THE TIME THE CTLRS SOUND PERTURBED IF PLTS MAKE RPTS OVER THE COMPULSORY LOCATIONS. IN THIS INSTANCE; THE CTLR SOUNDED UPSET WITH THE RPT OVER REPIS. THE RPTR SAID FROM NOW ON HE WILL BE MAKING POS RPTS OVER ALL OF THE COMPULSORY LOCATIONS UNLESS HE KNOWS THEY HAVE BEEN RADAR IDENTED.