CLRNC CONFUSION FOR ACR ON ARR TO MONTEGO BAY.

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DURING DSCNT INTO MONTEGO BAY; JAMAICA; KINGSTON CTR ADVISED US TO: 'CLRED TO FL90 AND CLRED FOR THE FROST 5 ARR.' RADIO CONTACT WAS LOST WITH KINGSTON CTR AND WE WERE WELL INSIDE 'FROST' AT FL90. WE REGAINED RADIO CONTACT WITH KINGSTON AND ASKED HIM IF WE SHOULD BE ON MONTEGO BAY APCH/TWR. HE SAID IN A SURPRISED TONE 'AREN'T YOU THERE YET;' AND AFFIRMED WE WERE CLRED FOR THE FROST 5 ARR. WE WERE IN THE TURN TO THE 12 DME ARC AND STARTED DSNDING TO 3000 FT AT MOBAR WHEN WE CONTACTED MONTEGO BAY APCH/TWR; AND TOLD HIM WE WERE OUT OF FL80 FOR 3000 FT. HE INFORMED US THAT WE WERE ONLY CLRED TO FL90. HE THEN CLRED US TO 3000 FT AND CLRED US FOR THE APCH. ON TAXI IN HE ASKED US FOR OUR ACFT REGISTRATION NUMBER AND WHEN QUERIED WHY HE STATED WE HAD VIOLATED THE APCH CLRNC ALT FROM KINGSTON CTR. SUBSEQUENT FACE-TO-FACE DISCUSSION WITH THE APCH/TWR/GND OPERATOR REVEALED THAT THIS ALT PROBLEM WAS COMMON. HE WAS NOT GONG TO VIOLATE US BUT WAS GOING TO ENTER THE INCIDENT IN HIS LOG. HE AGREED THAT THE WORDING WAS CONFUSING TO PLTS. KINGSTON CTR'S DIRECTION TO MAINTAIN FL90 AND CLRED FOR THE FROST 5 ARR LED US TO BELIEVE WE WERE CLRED FOR THE FROST 5 ALTS ALSO. NOT SO. HAD HE SAID CLRED FOR THE FROST 5 BUT MAINTAIN FL90; THIS WOULD HAVE CLARIFIED THE ISSUE. HAVING JUST RETURNED FROM SEVERAL TRIPS TO PARIS; FRANCE; WE ARE EXPECTED TO FLY THE STAR EXACTLY AS PUBLISHED UNLESS TOLD OTHERWISE. THIS MIND SET WAS STILL WITH THE PLTS CONCERNED. THE FROST 5 ARR SHOULD BE CLARIFIED; AT THE LEAST; THE NOTE FOR MOBAR AT 3000 FT SHOULD BE ELIMINATED. SUPPLEMENTAL INFO FROM ACN 210143: THE FO AND I THOUGHT WE HAD BEEN CLRED TO DSND AS DEPICTED ON THE FROST 5 ARR. I THINK SOME CONTRIBUTING FACTORS TO THE MISUNDERSTANDING COULD BE 1) LACK OF ATIS AT THE ARPT; 2) BEING CLRED FOR THE ARR RTE BUT NOT THE ALTS; 3) FATIGUE; FLYING ALL NIGHT; EARLY MORNING ARR; 4) UNFAMILIARITY WITH THE ARPT AND ITS ARRS AND PROCS.