Well Skip, I can spell it out for you in 2 different codes that I have handy now. ASME Sec. VIII /UW-35, Maximum reinforcement, there is a table in this section that gives max. reinforcement allowed based on thicknesses of base material. For example for thickneeses over 3/16" up to and including 1/2" , reinforcement up to 5/32 is acceptable and the table progresses to an acceptable reinforcement of 5/16" for thicknesses over 5".
ASME B31.3 TABLE 341.3.2 (L) , there is a table very simillar to the one above but the acceptable limits are different: For example thicknesses greater than 1/4" and less than or equal to 1/2" has an acceptable limit on reinforcement of 1/8" and the table prgresses to :thicknesses greater than 1" allow 3/16" reinforcement. Any inspector that deviates from these acceptance criterias should be challenged , unless the customer specifications state a more stringent criteria.
The main thing you need to know is what code you are welding to and what is acceptable prior to making the weld. If you ask the inspector he / she should be be able to give you a cut and dry answer on this issue, if the inspector can`t give you a strait answer, then you simply have an inspector problem.