VFR BE90 ISSUED CLASS C TRANSITION CLRNC; SUBSEQUENTLY QUESTIONED BY SECOND CTR.

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WE WERE ON A VFR XCOUNTRY TRAINING FLT FROM DED TO MTH. GOING DOWN THE FLORIDA EAST COAST; WE GOT IN CONTACT WITH PBI APCH CTL ON 124.6 ABOUT 25 NM N WHILE WE WERE IN A VFR DSCNT GOING THROUGH ABOUT 6500 FT AND TOLD THEM WE WOULD LIKE TO GO VFR DOWN THE SHORELINE. THEY APPROVED THAT OP TO REMAIN BELOW 1000 FT. WE ASKED IF THAT WAS A CLRNC INTO THEIR CLASS C AIRSPACE; AND THE CTLR SAID 'AFFIRMATIVE; YOU ARE CLRED INTO THE CLASS C TO FLY DOWN THE SHORELINE BELOW 1000 FT.' ABOUT 3 NM NE OF THE ARPT; AS WE WERE LEVELING JUST BELOW 1000 FT; WE GOT A FREQ CHANGE TO ANOTHER CTLR. WE CHKED ON 'AT 1700 FT DSNDING TO BELOW 1000 FT.' THE CTLR WAS EITHER BUSY OR DISTR WITH SOMETHING ELSE; BECAUSE HE DIDN'T ACKNOWLEDGE. WE CALLED AGAIN 'AT 1600 FT DSNDING BELOW 1000 FT' (WE MAY HAVE HAD TO MAKE A THIRD CALL; I CAN'T REMEMBER). WHEN THE CTLR FINALLY TALKED TO US; WE WERE JUST OFF THE SHORELINE LEVELING AT JUST BELOW 1000 FT; AND WE WERE JUST N OF THE FINAL APCH COURSE FOR RWY 27R; WHICH WAS THE ACTIVE. DURING THE WHOLE EVOLUTION; WE WERE WATCHING A B737 GETTING VECTORED FOR APCH TO RWY 27R. WHEN THE CTLR FINALLY TALKED TO US; IT WAS WITH SOME URGENCY HE GAVE US A VECTOR TO 220 TO GO DOWN THE INTRACOASTAL. THAT PUT US AND THE B737 ON COURSES TO THE SAME HUNK OF AIRSPACE AT THE SAME TIME. HE WAS ON A DSCNT FOR APCH; SO WE CLBED A LITTLE AND WENT OVER TOP OF HIM ABOUT 500 FT ABOVE HIM. THE CTLR ASKED US 'WERE YOU EVER AT 2000 FT?' WE TOLD HIM WE WERE CLRED DOWN THE SHORELINE BELOW 1000 FT; AND HE ASKED AGAIN 'WERE YOU EVER AT 2000 FT?' WE DIDN'T KNOW EXACTLY HOW TO RESPOND; BECAUSE OF COURSE; WE CLBED THROUGH 2000 FT ON DEP FROM DED; AND WE DSNDED THROUGH 2000 FT WHEN WE GOT CLRED INTO THE CLASS C TO GO DOWN THE SHORELINE BELOW 1000 FT. IN RETROSPECT; HE MAY HAVE BEEN ASKING IF WE HAD BEEN ASSIGNED TO MAINTAIN 2000 FT; WHICH WE HAD NOT. I WAS SURPRISED THE CTLR NEVER JUST TOLD US TO WIDEN OUT TO THE E A LITTLE FARTHER OFF SHORE TO PASS BEHIND THE B737. I BELIEVE THE 2 APCH CTLRS HAD DIFFERENT IDEAS OF WHAT WE WERE DOING. THE SECOND CTLR DID NOT UNDERSTAND WHAT THE FIRST HAD CLRED US TO DO. THERE WAS A HDOF PROB.