Client's approval is not relevant. It is important to know if the proof and the print results are correct, so I agree with Stephen, you need to be able to measure them. It is also important the proofing substrate used. I have extracted this text from the eci.org website: "Another specific characteristic applies to proofing for offset printing on uncoated stock: Using a semi-matt proofing substrate, commonly used for “coated” proofs, will yield a poor visual proof to print match even in the case of an excellent metered proof evaluation. The use of uncoated proofing stock results in the best possible metered match with the aim values of the characterization data set and the best possible visual proof to print match."
And for the paper white, some vendors have solutions; f.i. GMG and the Paper Adaption Tool for the calculation of the paper tint correction, resulting in a better match of proof and print.