A BE76 PLT; ALONG WITH 2 FELLOW PLTS; USING A NEARBY ARPT'S ATIS INFO; DEPARTED RSW WITHOUT A CLRNC.

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I WAS R-HAND SEAT IN A BEECH DUCHESS ON MAY/SAT/02. IN THE L-HAND SEAT WAS MR X AND IN THE BACK WAS MR Y. I HAD BEEN PIC UNTIL RSW BUT HAD SWAPPED SEATS WITH MR X AT RSW. AS WE TAXIED TO THE EDGE OF THE APRON (I WAS DOING THE RADIO); I REQUESTED THE ATIS FREQ FROM MR Y WHO WAS HOLDING THE PLATES IN THE REAR OF THE ACFT. HE MISTAKENLY GAVE ME THE FREQ FOR PAGE FIELD. HE WAS MISTAKEN AS THE COMMERCIAL PLATE USED SHOWED FT MYERS AS THE AIRFIELD IN THE TOP R SIDE. I DIALED IN 119.00 AND ATIS 135.2 WHICH STATED AIRFIELD'S HRS OF OP. I DID NOT QUESTION THE FREQ AND WE ALL AGREED THAT THE AIRFIELD WAS CLOSED (WE WERE USED TO AIRFIELDS BEING CLOSED AT NIGHT; IE; FPR VRB). WE; THEREFORE; XMITTED ON THE CTAF FREQ 119.00 AND PROCEEDED TO DEPART. THIS WAS AT XA15 HRS. WE DID THE PRETKOF CHKS AND WAITED TO GET ONTO THE RWY. AT THIS TIME; MR X HAD THE PLATE IN HIS POSSESSION AND I WAS SURPRISED WHEN AN ACR BRASILIA LANDED WITHOUT MAKING ANY CALLS. WE BEGAN OUR TKOF ROLL MAKING CALLS ON CTAF. THE TKOF WAS ABORTED DUE TO THE DOOR COMING OPEN ON THE PORT SIDE. WE TAXIED BACK AND DEPARTED RSW. WE DID SEE OTHER TFC ABOUT 10 MI AWAY ON FINAL; BUT DID NOT CONSIDER THIS A FACTOR; THEN WE DEPARTED. ON SPEAKING TO APCH; WE WERE TOLD OF OUR MISTAKE. SUPPLEMENTAL INFO FROM ACN 548681: AS BACK SEAT PAX; UNFAMILIAR WITH FT MYERS AREA; IN DARK ENVIRONMENT; ACCIDENTALLY READ ATIS FROM FT MYERS APCH PLATE. BUT FT MYERS PAGE ARPT CLASS D 8 NM NW OF OUR ARPT. AFTER VMC DEP WE CONTACTED APCH AND THERE THE MYSTERY UNFOLDED. WE WERE ASKED TO PHONE FT MYERS AFTER LNDG.