I find the entire process baffling. If the insurance company's reviewer agreed with the value, despite disagreeing with the appraiser's data and/or methods, why is there any issue at all? As long as the value is there, from the insurer's perspective, what additional risks does the insurance company have to bear? It seems as though the PI co is attempting to rescind coverage over an irrelevant technicality.
One might argue that the unacceptable appraisal demonstrates lax diligence on the part of the lender, which could lead to real issues later on... I'm not sure that argument carries a whole lot of water, though...
***************************************
The original post raises a question. I see the reviewer didn't present alternative supporting data for his/her conclusion. Did he/she at least include any discussion of what specifically was found lacking in the data that was dismissed?