Your situation depends a lot on the definition of "fair market value". Unfortunately, many realtors/agents use the term "fair market value" or "market value" as a sales pitch to win over buyers/sellers, when in reality they are referring to "sale price" or "purchase price". The bank is using a definition of "fair market value" as defined by the Appraisal Institute and Uniform Standards of Professional Appraisal Practice which is widely used by all banks, lenders, GSEs, FHA/VA, state and federal regulations for valuations of federally funded real estate transactions or related transactions.
While a lot of banks do use BPOs and/or CMAs for a suggested sales or list price, prepared by sales people to obtain the listing, they also obtain full appraisals from licensed/certified appraisers on properties to determine the "market value" or "fair market value". A majority of my business has been and is doing appraisals on preforeclosure, short sale, and foreclosed properties requested on behalf of banks.
It is also quite common for banks not to accept less than 80 - 85% of the appraised market value. The appraisal (by an independant third party) takes into account and consideration far more data and information then what a sales person is willing, capable, or licensed to do, thereby providing a more accurate and justifiable value conclusion. Sales people pretty much only provide data that supports their price,