B737-700 CREW REFUSED ATCT LCL CTLRS CLRNC TO TAXI INTO POS AND HOLD ON RWY 24L; AFTER A LNDG MD11 APPEARED TO BE LINED UP FOR THE RWY. THEY ALSO REFUSED TO CROSS THE RWY FOR THE SAME REASON. AFTER THE LCL CTLR FINALLY CLRED THE B737 FOR TKOF ON RWY 24R; THE CREW BEGAN TO TAXI ACROSS RWY 24L; THE CTLR THEN TOLD THE CREW TO 'STOP IMMEDIATELY.' BY THAT TIME THEY WERE ABOUT 5 FT PAST THE HOLD LINE.

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WE WERE CLRED TO TAXI OUT FROM GATE TO 'FOLLOW ACR Y TO RWY 24L VIA TXWY E.' ACR Y IMMEDIATELY TOOK OFF. WE FOLLOWED ACR Y UP TO THE RWY 24L HOLD SHORT LINE; SINCE AFTER ACR Y TOOK OFF; WE WERE THE ONLY ACFT ON THAT SIDE OF LAX. WE HELD AROUND 7 MINS WAITING FOR TKOF. IN THIS TIME ONLY AN L1011 LANDED. WE WERE WONDERING; 'WHY ARE WE WAITING SO LONG FOR A TKOF CLRNC?' I ASKED THE CAPT; 'SHOULD I LET TWR KNOW WE ARE READY FOR TKOF?' ABOUT THEN; LAX TWR TALKED TO AN MD11 ON FINAL FOR RWY 25'S; 'ARE YOU SURE YOU ARE ON FINAL FOR RWY 24R?' THE MD11 BANKED PRETTY GOOD FOR RWY 24R. IT LOOKED LIKE HE WAS NOW ALIGNED FOR RWY 24L. BOTH THE CAPT AND I WERE CONCERNED. (IT WAS QUITE HAZY THAT DAY; A LOT MORE THAN THE 'OFFICIAL' 8 SM.) THEN TWR TOLD US TO 'GET INTO POS AND HOLD FOR RWY 24L.' CAPT SAID 'NO' AND I AGREED. WE TOLD ATC 'NO;' DUE TO THE SIT. TWR TOLD US 'WE APPRECIATE YOU WATCHING OUT THERE' (IN REF TO US WATCHING PLANES ON FINAL AND MAKING SURE IT WAS SAFE TO TAKE A RWY) AND THEN SAID TO 'CROSS RWY 24L AND HOLD SHORT OF RWY 24R.' CAPT THEN SAID; NO; SINCE WE WERE STILL NOT SURE OF THE MD11; AND WHAT HE WAS DOING. TWR WANTED TO KNOW WHY? I TOLD THE CAPT; 'YOU TALK TO THEM.' HE STARTED TO TELL THEM WHY; AND THEN WE COULD CLRLY SEE THE MD11 WAS NOW LINED UP FOR RWY 24R. SO CAPT SAID WE WOULD ACCEPT RWY 24R AND WE STARTED TO TAXI CROSS RWY 24L FOR RWY 24R. THEN AFTER WE WERE 5 FT PAST THE HOLD SHORT LINE OF RWY 24L; TWR THEN SAYS FOR US TO 'HOLD SHORT OF RWY 24L.' I WAS GOING TO IMMEDIATELY TELL TWR THAT WE WERE NOW 5 FT PAST THE HOLD LINE (AS PER THE PREVIOUS CLRNC TO CROSS FOR RWY 24R). THEN TWR SAID QUICKLY; 'POS AND HOLD RWY 24L.' SO WE HELD IN POS. THEN TWR MENTIONED; 'IN THE FUTURE; WAIT AT THE TWR FREQ SIGN AND TXWY V.' AND THEN HE CLRED US FOR TKOF RWY 24L. I ACKNOWLEDGED HIM AND THE TKOF AND REST OF THE TRIP WAS NORMAL. CAPT AND I DISCUSSED IT A LOT. HE SAID; 'NEVER IN MANY YRS OF FLYING IN AND OUT OF LAX HAS HE HAD SOMETHING LIKE THAT SAID BY ATC.' USUALLY GND ALWAYS TELLS YOU TO GO TO THAT LINE OR THE CONCRETE PAD. THEY DID NEITHER; AND SINCE THE ARPT WAS EMPTY; WE PRESUMED THEY MEANT IT. WE FOLLOWED EXACTLY WHAT THEY SAID TO DO. THE COMMERCIAL CHART ARPT PAGE SAID NOTHING OF THIS. NEXT TIME; I WILL INQUIRE GND OR TWR; IF THEY FORGET TO TELL US TO HOLD AT THIS LINE OR SPOT; WHICH IS AHEAD OF THE RWY 24L HOLD LINE. PLUS IT WOULD HAVE BEEN A LOT BETTER IF TWR WOULD HAVE TOLD US WHAT TO DO 'IN THE FUTURE' WHILE WE WERE WAITING FOR AROUND 7 MIS AT THE (WHILE IT WAS QUIET) HOLD SHORT LINE; THEN RIGHT AT TKOF. DOING WHAT THEY DID; COULD EASILY THROW YOU OFF MENTALLY OF THE TASK AT HAND.