FINAL APCH RWY CHANGE FORCING GAR. CONFLICT IN CLB. FUEL SVC QUESTIONED.

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DEPARTED IAD AT XA16Z FOR MMMX. UPON ARR; ATIS INDICATED RWY 23L APCHS IN USE. WE WERE CLRED FOR APCH WHEN; AT 1000 AGL; WE WERE ISSUED A GAR BECAUSE THE ARPT WANTED TO SWITCH RWYS TO 5R. WE FLEW INITIAL PUBLISHED MISSED APCH PROC BEFORE BEING ASSIGNED VECTORS TO INTERCEPT 5L ILS APCH. WHEN ESTABLISHED ON APCH; WE WERE ISSUED ANOTHER GAR BY APCH CTL BECAUSE OF AN EMER ON RWY 5L. WE WERE ASSIGNED SEVERAL VECTORS FOR AN EVENTUAL HOLDING PATTERN AT OTU VOR. ON ONE VECTOR; APCH CLRED US TO 12000 FT. PASSING THROUGH 11000 FT OUT TCASII ADVISED US OF TFC AT 12 O'CLOCK CLBING THROUGH 12000 FT. WE LEVELED AT 11200 AND TOLD APCH CTL OF OUR TFC. WE WERE TOLD HE WAS CLBING TO 13000 FT (HOWEVER OUR VERT CLB WAS MUCH HIGHER RATE). IF NOT FOR TCASII AND VISUALLY ACQUIRING THE TFC; WE WOULD HAVE COME VERY CLOSE TO THE TFC; IF NOT HIT IT. WE HELD (1 TURN) AT OTU; THEN GOT VECTORS AGAIN TO 5L; WHERE WE LANDED AT XE54Z. WE BLOCKED IN AT OUR GATE AT XE59Z WITH 9000 LB FUEL. OUR FAR FUEL WAS 4700 AND ALTERNATE (ACA) FUEL OF 4400 LB. OUR FLT WAS TO CONTINUE TO MROC (SAN JOSE; COSTA RICA) WHEN THE MEXICAN AVIATION AUTH WOULD NOT ALLOW US TO BOARD FUEL. AN OFFICIAL CAME TO COCKPIT AND RECORDED OUR BLOCK-IN FUEL AND TOOK A COPY OF OUR FLT PLAN (IAD-MEX); THEN WE WERE ALLOWED TO BOARD FUEL. OUR SUBSEQUENT FLT WAS UNEVENTFUL.