NEC 250.53 (A)(2) Exception gives you the out if you can test and prove less than 25 ohms resistance to earth. However 90.4 gives the AHJ permission to add or delete or not accept the NEC. The AHJ (Inspector) has the last say and there could be a local code that requires the extra ground rod. I would simply ask why he is requiring this and discuss with him NEC 250.53 (A)(2) exception (be ready to be able to test the current grounding electrode system to be able to prove the less than 25 ohms to earth), but if he requires it I would suggest just installing it as it will not hurt and will save you pain and suffering in the future. Now don't get me wrong if there is an inspector that is requiring something other than what the NEC says (which NEC is just the minimum requirements) that is a danger or that is below the minimum requirements of the NEC then I would say that is a worthy fight. IMOIf the CE electrode was properly installed and inspected the NEC does not require the ground rod. I would not humor him and install one just on principle. We have a big problem in this country (and getting worse by the day) with incompetent inspectors (and trades people in general) and I'm not inclined to bolster their incompetence by adhering to things they just make up.