A CL65 CREW EXPERIENCED PRESSURIZATION PROBS AND CONDUCTED AN EMER DSCNT. SUBSEQUENTLY; AS THE FLT CREW WAS ATTEMPTING TO RECEIVE ATIS INFO; THE FLT WAS ORDERED TO AN ALTERNATE ARPT.

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AT FL370; SMOOTH RIDE; RECEIVED R PACK HIGH TEMP MASTER CAUTION. CAPT REQUESTED DSCNT TO FL250 WHILE FO RAN CHKLIST. R PACK HIGH TEMP MASTER CAUTION WENT OUT. PACK DID NOT RESET OR COME ON. CABIN ALT REMAINED STEADY (+200 FT). CABIN DIFFERENTIAL WAS STEADY. UNEVENTFUL DSCNT TO FL250. UPON LEVELING AT FL250; APPLYING PWR AND STABLE; RECEIVED L PACK HIGH PRESSURE. CAPT REQUESTED 'EMER DSCNT.' FO RAN CHKLIST. DSCNT INITIATED TO 10000 FT. AIR EMER DECLARED. L PACK RESET ITSELF. RESUMED NORMAL OPS. APPROX 160 NM FROM ZZZ; ATTEMPTED TO OBTAIN ATIS. WE WERE TOO LOW OF AN ALT TO RECEIVE IT. REQUESTED CTR TO RETRIEVE ATIS WX AND ATIS LETTER FOR INITIAL CONTACT WITH APCH. WE WERE TOLD; 'UNABLE THAT INFO;' AND COULD RECEIVE AWOS WX INSTEAD. CREW ACKNOWLEDGED OK. VERY SOON AFTER; A DIFFERENT VOICE CTLR ON CTR CAME BACK TO US WITH A COMMENT REGARDING OUR STATUS THAT FLT CREW WAS CONFUSED BY. NO OTHER REF WAS MADE AS TO OUR STATUS ON CONTINUING ON TO ZZZ. UPON ARR TO APCH CTL AIRSPACE; AFTER JUST SWITCHING FROM CTR FREQ TO APCH FREQ; LISTENED TO ATIS AND RECEIVED ATIS LETTER CODE TO USE ON INITIAL CALL WITH APCH. ON INITIAL CALL WITH APCH; WE WERE GIVEN VECTORS/HDGS TO ZZZ WHILE ON THE DOWNWIND TO RWY 1 AT ZZZ ON A HDG OF 150 DEGS AND TOLD TO EXPECT VISUAL RWY 1. WAITING FOR AN APCH CLRNC; APCH ADVISED US THAT WE WOULD NOT BE LNDG AT ZZZ AND EXPECT VECTORS TO LAND AT ZZZ1. VECTORS WERE ISSUED AND NORMAL APCH AND LNDG WAS ACCOMPLISHED. UPON ARR AT ZZZ1; WE WERE INSTRUCTED TO TAXI TO THE RAMP. MEANWHILE; NO OTHER INFO WAS GIVEN TO FLT CREW AS TO WHAT WAS GOING ON. TAXIED TO THE RAMP; INSTRUCTED TO TALK TO ARPT OPS IN THE FOLLOW-ME TRUCK; AND WAS TOLD TO SHUT DOWN AND PARK AND MEET SECURITY AT THE DOOR. LCL/ARPT POLICE CAME ONTO THE ACFT AND SEARCHED AND ASKED SECURITY QUESTIONS. AT THIS POINT; IT WAS TOLD TO THE FLT CREW AS TO WHY WE WERE DIVERTED TO ZZZ1 AND WERE ASKED TO SEE PROPER IDENT. UPON COMPLETION OF SECURITY INSPECTION AND QUESTIONS; WE WERE RELEASED TO THE GATE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT THE WRITTEN INVESTIGATIVE REVIEW HE RECEIVED INDICATED A CONFUSION AT THE ATC FACILITY OVER THE ATIS INFO REQUEST. ATC UNDERSTOOD THAT THE CREW WAS ASKING FOR THE ATIS INFO ALPHABET ASSIGNMENT LETTER (ALPHA; BRAVO; CHARLIE; ETC) WHEN IN FACT THE CREW WAS ASKING FOR THE ACTUAL RPTED WX CONDITIONS. UNCERTAINTY DEVELOPED OVER WHAT WAS SAID AND SOMEONE ORDERED THE FLT TO ZZZ1 PRIOR TO PROCEEDING TO ZZZ. ONLY AFTER THE TAPES WERE REVIEWED BY THE TSA; ATC; AND THE FLT CREW'S COMPANY DID THE EVENTS BECOME CLR AND THE CREW EXONERATED OF ANY WRONGDOING.