AFTER FREQ CHANGE THE APCH CTLR QUESTIONED THE CREW'S DSCNT.

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ON FLT ABC FROM BWI-LAX; OUR ORIGINAL CLRNC WAS THE CIVET 4 STAR TO LAX. ABOUT 200 MI FROM LAX WE WERE RECLRED DIRECT TNP FOR THE PDZ 3 STAR TO LAX. APCHING TNP; WE WERE CLRED TO DSND VIA PDZ 3 STAR TO EXPECT RWY 25L. WHILE ON THE ARR WE WERE VECTORED OFF COURSE FOR SPACING APCHING THE TRTLE INTXN. FOLLOWING THE VECTORS WE WERE RECLRED 'DIRECT PDZ AND DSND FOR THE APCH FOR RWY 25L.' THE SAME CTLR WAS WORKING US THE WHOLE TIME AND WE CONTINUED OUR DSCNT AND APCH. WHILE ON THE APCH TO RWY 25L WE WERE SWITCHED TO THE FINAL CTLR BTWN THE GATTE AND HUNDA INTXNS. AFTER CHKING IN THE FINAL CTLR QUESTIONED WHY WE HAD DSNDED OUT OF 8000 FT AT FUELR SINCE HE SAID THAT WAS OUR CLRNC LIMIT. WE RESPONDED THAT THE PREVIOUS CTLR HAD CLRED US FOR THE PDZ 3 ARR AND APCH TO RWY 25L. NOTHING ELSE WAS SAID UNTIL WE WERE SWITCHED TO TWR. WE WERE UNDER THE IMPRESSION WE HAD BEEN CLRED FOR THE ARR/APCH BY THE ORIGINAL CTLR; OTHERWISE WE WOULD NOT HAVE CONTINUED THE APCH. EITHER WE MISUNDERSTOOD OUR CLRNC AND/OR THERE WAS A BREAKDOWN IN COMS BTWN THE CTLRS. EITHER WAY IN THE FUTURE WE WILL RECONFIRM WITH THE CTLR PRIOR TO COMMENCING AN APCH TO LAX.