On the information given I believe I am correct and so is the inspector for failing the parts, to suggest you fire the inspector is IMO crazy.
Having said that I seriously doubt any true engineer or draftsperson would put a +/- .005 dimension on the depth of a thread, as it is near impossible to achieve or measure.
Again only my opinion but the solution to the problem is to get the drawing changed not buy some expensive gauges that would only prove that the tolerance is stupid, as stated in my original post.
This seems to be a growing problem at least in the UK that we are forced to chase stupid tolerances because no one can find an engineer that will sign off a change, surely the solution to all this should be no more than a phone call and or email?
Even worse than any of this is the attitude that I have a problem I cannot solve so I will fire the inspector who fails the parts given above.
People question why work is sent to the Far East and engineering is struggling in the USA and Europe, this is a perfect example we are handing it them on a plate.