A B737-300 FLT CREW IS CONCERNED WITH A TWR CTLR THAT ISSUES A HOLD SHORT CLRNC WITH ANOTHER ACR IN TKOF POS AT LAX. LCL CTLR PERCEIVED POSSIBLE RWY INCURSION THAT DID NOT OCCUR.

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THE FO FLEW AN ILS APCH TO RWY 7R AND TRANSITIONED TO A VISUAL APCH AT 1500 FT AGL. HE MADE A GOOD LNDG IN THE TOUCHDOWN ZONE AND STARTED TO SLOW THE ACFT ON THE RWY USING REVERSE THRUST AND AUTO BRAKES. THEN; AT APPROX 110 KTS; AND WHILE STILL IN THE LNDG PHASE OF FLT USING REVERSE THRUST; THE LAX TWR CTLR SAID 'ACFT X; TURN OFF AT TXWY G AND SAY GATE.' AT THIS POINT; WE WERE PASSING TXWY H (ABOUT 6000 FT DOWN THE RWY) AND TXWY G WAS LESS THAN 1000 FT AHEAD OF US; AND WE WERE STILL SLOWING THE ACFT DOWN. THE CAPT REPLIED TO THE CTLR 'ROGER; EXIT AT TXWY G AND GATE XX.' THE CAPT THEN SAID '80 KTS;' THEN '60 KTS; MY ACFT;' AND TOOK CTL OF THE ACFT FROM THE PF; THE FO. THE CAPT HAD TO AGGRESSIVELY USE WHEEL BRAKES TO SLOW THE ACFT ENOUGH TO SAFELY MAKE THE 90 DEG L TURN AT TXWY G. THE CAPT STOPPED THE ACFT ON TXWY G USING VERY FIRM BRAKING; AND HELD SHORT OF RWY 7L. THE LAX CTLR DID NOT SAY 'HOLD SHORT OF RWY 7L' UNTIL WE WERE ALREADY STOPPED SHORT OF RWY 7L. AT NO TIME DID ANY PART OF THE ACFT CROSS ANY PART OF THE HOLD SHORT LINE OR CROSS ONTO ANY PART OF RWY 7L. AFTER THE CTLR SAID 'HOLD SHORT OF RWY 7L' HE IMMEDIATELY SAID 'ACFT Y; TKOF CLRNC CANCELLED.' WE WERE UNABLE TO REPLY TO HIS FIRST INSTRUCTION TO HOLD SHORT DUE TO RADIO CONGESTION ON THE FREQ BY THE LAX TWR CTLR. THE ACFT WAS ALREADY STOPPED AND HOLDING SHORT OF RWY 7L WHEN THE CTLR SAID AGAIN 'ACFT X; HOLD SHORT OF RWY 7L.' AFTER THIS RADIO CALL; HE GAVE US THE TIME TO REPLY 'ACFT X IS HOLDING SHORT RWY 7L.' THE CTLR THEN TOLD US TO CROSS RWY 7L AND CONTACT GND. WE CROSSED THE RWY AND CONTACTED GND. AFTER WE CLRED RWY 7L; THE GND CTLR TOLD THE CAPT TO CALL THE LAX TWR FOR A POSSIBLE RWY INCIDENT. THE CTLR DID NOT TELL US HOLD SHORT OF RWY 7L WHEN HE TOLD US TO TURN OFF AT TXWY G; BUT WE KNEW TO HOLD SHORT ANYWAY; BECAUSE YOU ALWAYS HOLD SHORT OF THE RWYS AT LAX. AGAIN; WE HELD SHORT ON OUR OWN; BECAUSE OF OUR FAMILIARITY WITH LAX ARPT; BUT THE CTLR DID NOT TELL US UNTIL WE WERE ALREADY STOPPED. THIS ATC COM ERROR IS A SERIOUS SAFETY CONCERN HERE AT LAX. AGAIN; AT NO TIME DID ANY PART OF THE ACFT CROSS THE HOLD SHORT LINE FOR RWY 7L.