I always believe a market value opinion regardless of whop orders, it including a lender client or private client. But not every appraiser agrees - we've seen posts saying things like when it is a private client we can "think outside the box"
Well, no,- because an appraisal IS a box - a box of an accepted model of standards and SOW to get a credible result. .Sure, we can do whatever we want, such as go against what actual buyers behavior and use all cherry picked, less similar comps to get a desired $ result - but it will not be a credible appraisal.
Which goes back to clients - if the first appraisal was ordered by the lender, that was a not biased opinion (I use bias not racially, but the way non biased appears in the certs and standards, not the appraiser is not biased toward a value $ amount or direction or party or subsequent event ) The second appraisal, if it was ordered by the owner or attorney , (imo ) influence to achieve a result, which likely makes the appraisal not credible.