I would understand that your Client says that the vessel is designed according to ASME Section VIII, Division 1, better known as the "design by rule" or "design by formula" approach. Simplifying the discussion means it calls for simple and conservative mechanics formulas together with warnings regarding various effects(as nozzle loads, for example).
Division 2 of Section VIII calls for "design by analysis" as a need to develop pressure vessels that permit higher allowable stresses without compromising the safety. With Div 2 rules, we are able to calculate stresses "everywhere" in the vessel and the allowable is higher because we have confidence in the calculated values of stress.
May the value of the allowable stress be the basis of your Client objections? It is worth to discuss this aspect.
I think a good point in your discussion would be... OK, FEA is "design by analysis" but is WRC 107/297 "design by rule"? For me WRC 107/297 seem to be more "design by analysis" with the tools of '60s than "design by rules", so I think that what your Client says make sense just in case in the contractual specification they made clear they want WRC as basis for nozzle loads.
In the end, a nice article of Mr. Trevor Seipp (TGS4 in
http://www.eng-tips.com)
http://becht.com/blog/performing-an-fea-...u-2-g-component