A CE560 PLT EXPERIENCED A CLOSE ENCOUNTER IN SOCAL AIRSPACE WHEN THE ACFT CONTINUED ITS ORIGINAL CLRNC WHILE ATTEMPTING TO PROGRAM A REVISED ROUTING TO LAX.

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WHILE FLYING ASSIGNED RTE ALONG V388 TO INTERSECT V283; THE CTLR ASKED US TO BE PREPARED FOR THE BASET 2 ARR. I PULLED OUT THE CHART AND HE ASKED US TO FIND CACTS INTXN. HE THEN ASKED US TO FIND PDZ VOR. WE ACKNOWLEDGED THE VOR AND HE CLRED US DIRECT TO THE VOR. WHILE THIS DISCUSSION WAS GOING ON AND BEFORE WE COULD PUNCH IN THE FIX; THE ACFT MADE A 90 DEG L TURN FOLLOWING THE PREVIOUS CLRED RTE. THE CTLR MADE A XMISSION THAT WAS BLOCKED BY ANOTHER ACFT. I KEYED THE MIKE AND SAID 'BLOCKED;' TO WHICH HE REPLIED; 'ACR XXX; TURN R IMMEDIATELY; IMMEDIATE R TURN. ACR XXX TO A HDG OF 330 DEGS; TFC LESS THAN 1 MI GULFSTREAM 6 AT APPROX 12500 FT.' MY FO; WHO WAS FLYING; IMMEDIATELY BANKED HARD R TO THE HDG. AFTER TURNING TO THE HDG; HE AGAIN CLRED US DIRECT TO THE VOR. NO OTHER DISCUSSION WAS MADE. AFTER LNDG; I CALLED MY COMPANY AND THEN CALLED SOCAL APCH CTL AND SPOKE WITH MR X. THEY HAD ALREADY LOOKED INTO THE INCIDENT AND SAID WE WERE FLYING THE CORRECT RTE. THE CTLR THOUGHT WE HAD BEEN GIVEN ANOTHER RTE AND AS FAR AS THEY WERE CONCERNED WE HAD PASSED NO CLOSER THAN 3 MI AND THAT WAS THE END OF THE MATTER. WHILE FLYING IN THE LAX AREA; I'VE NOTICED ON NUMEROUS OCCASIONS SEVERAL RERTES MID-FLT. THIS GREATLY ADDS TO CONFUSION OVER YOUR CLRED RTE AND PLT WORKLOAD.