AN A320 ACR AT FL290 WAS VECTORED OFF THE KARLO SIX STAR FOR TFC. WHEN ARTCC RECLRED ACR BACK TO STAR; THE PF ASSUMED THEY HAD DSCNT CLRNC TO FL240 AND STARTED DSCNT. THE ACR RECEIVED A TCASII TA; OBSERVING TFC PASSING 600 FT BELOW THEM. ATC ASKED ACR TO VERIFY AT FL290 AND ACR ADVISED THEY WERE DSNDING THROUGH FL267. ATC ADVISED THEY HAD COME IN CONFLICT WITH ANOTHER ACFT AND WAS ASKED TO CALL ARTCC UPON LNDG.

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FLT FROM LAS TO PHX CRUISING AT FL290 ON STAR KARLO 6 BLD TRANSITION. ZAB VECTORED US OFF THE ARR. PNF (CAPT) WENT MOMENTARILY OFF FREQ AND RETURNED TO HEAR PF (FO) ACKNOWLEDGE DSCNT CLRNC TO FL240. PF THEN REPEATED THE CLRNC TO PNF AS DIRECT KARLO AND DOWN TO FL240. DURING THE DSNDING TURN; TCASII TA INDICATED TFC AT 4 O'CLOCK POS MOVING AWAY 600 FT BELOW. CTR ASKED IF WE WERE STILL AT FL290; PNF RESPONDED NEGATIVE; DSNDING THROUGH FL276. ATC STATED THAT WE SHOULD BE AT FL290 UNTIL CLR OF TFC; THEN CLRED US TO FL240. THE PF RPTED AFTERWARDS THAT ATC ISSUED CLRNC OF DIRECT KARLO; DSND TO FL240; AND TFC AT 12 O'CLOCK POS. PF READ BACK DIRECT KARLO; DSND TO FL240; THEN BEGAN THE R DSNDING TURN. CTR INDICATED A POSSIBLE CONFLICT AND GAVE US A PHONE NUMBER TO CALL. THE WATCH SUPVR IN THE SUBSEQUENT CONVERSATION WITH ARTCC SAID THE CTLR CLRED US DIRECT KARLO AND TO MAINTAIN FL290. IF THIS IS TRUE; THEN MY SUGGESTION WOULD BE THAT CTLRS NOT INCLUDE A STATEMENT IN A CLRNC TO MAINTAIN THE ALT A PLT IS MAINTAINING ANYWAY. IN THIS CASE; WE WERE HELD HIGH AND THE PF WAS EXPECTING TO BE CLRED FOR A DSCNT. WHEN THE CTLR MENTIONED THE TFC; THE PF REASONED THAT WAS WHY THIS CTLR HELD US UP; BUT GIVEN THE TURN; THERE WOULD BE NO CONFLICT NOW FOR A DSCNT. THE CTLR ON THE OTHER HAND WOULD BE LESS APT TO LISTEN FOR A DSCNT CLRNC READBACK WHEN HE HAD JUST PRESUMABLY SAID TO MAINTAIN FL290. I SUGGEST THAT AT NO TIME SHOULD A CTLR REITERATE A CLRNC THAT THE PLT HAS ALREADY COMPLIED WITH. THIS CAN ONLY OPEN OPPORTUNITY FOR ERROR.