B777 CAPT AND APCH CTLR DISAGREE AS TO SEVERITY OF CONVECTIVE WX AND APPROPRIATE ACFT TRACK IN THE VICINITY OF ORD.

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THE ORD APCH CTLR INSISTED WE TURN INTO CELLS PAINTING RED AND MAGENTA ON THE DOPPLER RADAR; INSISTING IT WAS 'ONLY LEVEL 2.' BOTH OUR AIRBORNE WX RADAR AND VISUAL INSPECTION OF THE CUMULONIMBUS CLOUDS INDICATED OTHERWISE TO ME; MY COPLT; THE FAA ACR INSPECTOR (FORMER AIRLINE PLT AND QUALIFIED ON THE ACFT) ON THE ONE JUMP SEAT AND THE COMPANY DISPATCHER ON THE OTHER. TO IMMEDIATELY COMPLY WITH THE ATC INSTRUCTIONS WOULD HAVE VIOLATED BOTH FAR'S AND COMPANY OPERATING GUIDANCE ON WX AVOIDANCE. THE CTLR CLAIMED THERE WAS 'TFC IN YOUR FACE' ON 2 DIFFERENT HDGS WHEN THERE WAS NEGATIVE TFC ON TCAS (I FULLY UNDERSTAND THE LIMITATIONS OF TCAS AS COMPARED TO ATC'S RADAR). IT APPEARED TO US; GIVEN THE LIMITATIONS OF TCAS; THAT WE WERE ENCROACHING UPON THE ORD DEP CORRIDOR WITH NO TFC PRESENT AND THE CTLR WANTED US BACK IN HER NORMAL ARR CORRIDOR WITH NO REGARD TO CONVECTIVE WX/HAIL. THE DIALOG FROM THE CTLR WAS NOT TYPICAL OF AN ORD CTLR; WHO ARE THE BEST IN THE WORLD. I THINK A REVIEW OF THE TAPES WOULD BE BENEFICIAL FOR ALL INVOLVED; INCLUDING ME.