FLC OF A B737-300 WERE QUESTIONED BY DEP CTLR REGARDING THEIR COMPLIANCE WITH SID TRACK. CTLR BELIEVED THAT THEY HAD NOT TURNED TO THE CORRECT HEADING WHICH WAS A HEADING FOR A DIFFERENT RWY. THE FLC COMPLIED WITH THE SID AND THE ADDITIONAL AMENDMENT GIVEN BY CTLR.

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AFTER DEPARTING LAS ON THE MEAD 1 DEP; THE CTLR SEEMED CONFUSED ABOUT OUR FLT PATH. HER FIRST RESPONSE AS WE CALLED WAS DID YOU DEPART RWY 19. WE REPLIED YES. WE WERE FLYING THE MEAD 1 SID WHEN SHE ASKED US IF WE HAD THE MEAD 1 ON BOARD. WE SAID YES. SHE INSTRUCTED US NOT TO TURN TOWARD BLD UNTIL PASSING 9000 FT WHICH WE DID. SHE ASKED US TWICE ABOUT NOT FLYING A 070 DEG HDG AND NOT TURNING TOWARD BLD EARLIER. THE 070 DEG HDG IS FOR RWY 25 NOT RWY 19 AND WE TURNED TOWARD BLD AT THE TIME SHE TOLD US TO (AT 9000 FT MSL). WE WERE FLYING THE SID AS DEPICTED FOR RWY 19 AND SHE KEPT ASKING US QUESTIONS THAT APPLIED TO RWY 25. THE CTLR CAUSED A LOT OF CONFUSION ON OUR PART BECAUSE WE DIDN'T UNDERSTAND WHY SHE KEPT ASKING ABOUT PROCS THAT APPLIED TO RWY 25 AND NOT RWY 19. WE DEPARTED RWY 19 AND FLEW SID AS IT WAS DEPICTED. SHE WAS VERY CONFUSED AND WITH THE LARGE HILLS AROUND LAS. THIS WAS NOT SAFE. SUPPLEMENTAL INFO FROM ACN 390860: I BELIEVE THAT SHE WAS EXPECTING US OFF OF RWY 25 OR AT LEAST EXPECTED US TO BE FLYING THAT TRANSITION. HER HANDLING OF THE SITUATION INCREASED THE STRESS AND WORKLOAD IN THE COCKPIT AT A CRITICAL PHASE.