ZID CTLR CHALLENGES F100 FLC ABOUT WX DEV.

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WE WERE FLT PLANNED LGA J6 AIRWAY TO LIT-DAL AT FL280. WE HAD WX (TSTMS) BTWN PERKS AND YOCKY INTXNS ON J6. WE ASKED ZID FOR A WX DEV L OF COURSE (J6). ZID SAID 'CLRED TO DEVIATE L OF COURSE; GO DIRECT TO LIT WHEN ABLE.' I READ BACK THE CLRNC. AFTER ABOUT 10-15 MINS OF CIRCUMNAVING THE WX ABOUT 13-25 NM L (S OF COURSE); ZID ASKED WHEN WE COULD GO TO LIT. I SAID IN A COUPLE OF MINS; THAT WE HAD ONE MORE TURN AROUND THE WX. THE TSTMS WERE SCATTERED IN THIS CLUSTER; AND THE TSTMS WERE SEPARATED ABOUT 20 NM APART WITH TOPS AT ABOUT FL300. THE TSTMS WERE NOT SEVERE. ZID THEN ASKED IF WE HAD TURNED R OF COURSE. I SAID NO; WE WERE STILL 20 NM L (S) OF J6. WE TURNED L TO CIRCUMNAV WX THAT WE WOULD HAVE TO TURN R TO GO DIRECT TO LIT. ZID THEN SAID THAT WE HAD TURNED R OF COURSE WITHOUT PERMISSION. I CAME BACK AND SAID THAT WE HAD NEVER CROSSED R OF THE PREVIOUS COURSE. I SAID WE HAD STAYED AT LEAST 13 NM L OF COURSE AND THAT WE WERE NOW CLR OF THE WX AND READY TO GO DIRECT TO LIT. ZID AGAIN CALLED BACK TO SAY THAT WE HAD NOT FOLLOWED HIS CLRNC. I SAID THAT ALL OF OUR INSTS SHOWED THAT WE HAD NOT CROSSED J6 AND THAT WE STAYED WITHIN 13-25 NM L OF COURSE AS PER OUR CLRNC TO DEVIATE FOR WX. THE CTLR GOT INTO A LENGTHY DISCUSSION ABOUT THIS CLRNC. I ASKED IF THERE WERE ANY OTHER ACFT AROUND US. ZID SAID THAT THERE WERE NO OTHER ACFT AROUND US. I DO NOT KNOW WHAT THE CTLR WAS THINKING; BUT WE HAD CLRNC TO DEVIATE L OF COURSE J6 FOR WX AVOIDANCE. IF THIS IS NOT PROPER PROC IN FOLLOWING THIS CLRNC; THEN I BELIEVE MOST PLTS OUT THERE DO NOT UNDERSTAND THIS TYPE OF FAA CLRNC FOR WX AVOIDANCE. I BELIEVE THAT THIS IS A PROB THAT NEEDS TO BE ADDRESSED BY UNION AND AIRLINE.