LGT HAS LTSS WITH SECOND ACFT IN PCA.

Narrative

FLT WAS CLBING N OUT OF MEXICO CITY TO FL330. AS WE POPPED OUT ON TOP AT AROUND 27000 FT WE NOTICED TFC AT 12 O'CLOCK. WE TURNED ON OUR LNDG LIGHTS AND GOT NO RESPONSE FROM THE TFC. CLBING OUT OF FL296 I QUESTIONED CTR ABOUT THE TFC. HE IMMEDIATELY TOLD US TO DSND TO FL290. I THEN ASKED WHAT ALT THE ACFT WAS AT; AND ADVISED HIM WE HAD BEEN CLRED TO FL330. THE ACFT WAS AT FL310. BY FL298 WE HAD REVERSED OUR CLB AND DSNDED TO FL290. AT NIGHT IT IS VERY DIFFICULT TO JUDGE DISTANCES OR DIRECTION OF FLT AND HAD THIS OCCURRED DURING DAY VFR WE WOULD NOT HAVE WAITED TO TAKE CORRECTIVE ACTION. WE CROSSED UNDER THE ACFT AT A VERT SEPARATION OF 1500 FT AND HORIZLY AT 5000 FT. AFTER THIS HAPPENED; I GOT ON CTR FREQ AND CHEWED OUT THE CTLR FOR NOT HAVING BETTER SEPARATION. THE CTLR HAD NO RESPONSE AND BASICALLY IGNORED MY REMARKS. THE PRIMARY CONCERN I HAD WAS THE LACK OF SEPARATION AND NOT RECOGNIZING THE PROB TILL WE BROUGHT IT UP. THE OTHER CONCERN WAS THAT OUR OWN DISPATCHER HAD FILED US FOR FL310; WHICH IS THE WRONG FLT LEVEL FOR OUR DIRECTION OF FLT (NE). WE; AS A CREW; CAUGHT THE MISTAKE AND THE INITIAL MEXICO CITY CTR CTLR CAUGHT IT AND CLRED US TO A CORRECT ALT OF FL330. HAD NEITHER ONE OF US NOT CAUGHT THE MISTAKE WE WOULD HAVE BEEN CLRED TO FL310 AS THE FLT PLAN SHOWED; AND BEEN IN DIRECT CONFLICT WITH THE OPPOSITE DIRECTION TFC. I FEEL THAT WAS THE MORE SEVERE SIT THAT COULD HAVE HAPPENED; BASED ON THE LACK OF SOPHISTICATION OF THE MEXICAN AIRSPACE. THE FLT CONTINUED ON TO DEST WITHOUT FURTHER INCIDENT.