B767 WITH ARTCC AT FL300 ALTERED COURSE FOR WX; WHEN QUESTIONED BY ATC AS TO EMER DECLARATION; RESPONDED IN THE AFFIRMATIVE.

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WE WERE IN A DSCNT FROM OUR CRUISE ALT OF FL390 TO CROSS 30 NM W OF ZZZ VOR AT FL250. THAT CLRNC WAS GIVEN VERY LATE FOR US AND I COULD SEE WE WERE GOING TO HAVE TROUBLE MAKING THE RESTR. WE INFORMED CTR OF OUR TROUBLE; AND ASKED IF WE COULD CROSS ZZZZZ INTXN AT FL250. THIS WAS THE NORMAL XING POINT AT WHICH WE HAD PLANNED ON XING AT FL250. CTR GRANTED OUR REQUEST AND SWITCHED OUR VHF FREQ. WE WERE DSNDING AS FAST AS WE COULD THROUGH AN OVCST LAYER OF CLOUDS WITH OUR SPD BRAKES FULLY EXTENDED TO MAKE THAT RESTR. WE CALLED ARTCC AND CHKED IN. ARTCC ACKNOWLEDGED AND GAVE US A FURTHER DSCNT TO FL240. WE READ BACK THE CLRNC AND BROKE OUT OF THE OVCST LAYER TO FIND OURSELVES HEADING DIRECTLY TOWARD A LARGE TOWERING CUMULUS BUILDUP AND WE ASKED CTR FOR A R DEV OF 10 DEGS. WE WERE RAPIDLY DSNDING OUT OF FL300 AND THEY CLRED US TO DEVIATE OUT OF FL280. I TOLD THE COPLT AS I TURNED R 10 DEGS WE HAVE TO TURN NOW AS WE WERE ONLY 1 MI OR 2 FROM PENETRATING THE LARGE TOWERING CLOUD. AS THE FO WAS GETTING READY TO CALL; CTR CALLED AND ASK IF WE HAD BEGAN OUR TURN AND ARE WE DECLARING AN EMER. I WAS RATHER STUNNED AND REPLIED 'YES.' THIS ALL HAPPENED VERY QUICKLY; A LOT OF EVENTS COMPRESSED INTO A FEW SECONDS. AS MIGHT BE EXPECTED; I SAW MY JOB WAS TO SAFELY MANEUVER THE ACFT AROUND THIS POTENTLY DANGEROUS SITUATION ASAP. WE FEEL WE ATTEMPTED TO INFORM ATC AS QUICKLY AS POSSIBLE; HOWEVER; THEY BEAT US TO THE CALL. WE WERE GIVEN A FREQ CHANGE TO APCH AND THEY LATER GAVE US A PHONE NUMBER TO CALL ARTCC ON THE GND. WE LANDED AT ZZZ RATHER CONFUSED ON WHAT HAD JUST HAPPENED. WE SHUT DOWN THE ENGS AT THE GATE; FINISHED THE CHKLIST; AND DEBRIEFED ABOUT WHAT HAD JUST TAKEN PLACE. WE THOUGHT THE CTLR MIGHT HAVE BEEN A TRAINEE AND JUMPED THE GUN A LITTLE QUICKLY. WE WERE VERY BUSY IN THE DSCNT AND TRIED OUR BEST TO COMPLY WITH HER INSTRUCTIONS AS QUICKLY AND SAFELY AS WE COULD PROCESS THE INFO AND FLY THE AIRPLANE. NEXT; I CALLED THE PHONE NUMBER AND TALKED TO WHO I THINK WAS A SUPVR. HE WAS VERY AGGRESSIVE ON THE PHONE ABOUT US NOT COMPLYING WITH THE CLRNC; BUT SAID BECAUSE HIS CTLR HAD DECLARED THE EMER FOR US HE WAS WILLING TO LET IT GO. THIS CONFUSED ME MORE; AND AFTER PROTEST JUST LET IT GO.