I wouldn't be so hard-lined NO on that one. I have in fact paid more (not a lot, but some) and bought a FANTASTIC deal! Appraisals are nothing more than an opinion thats based upon either NOI (5+ unit commercial deals, not much opinion there but CAP rates play into what one thinks its worth), or comparable sales or 'like' properties in the general area (and somewhat recent too).
Couple times its been nothing but "Hooey" to me... couple years back I bought a duplex - by luck of the draw the seller got a HORRIBLE appraiser (and appraisal), I got one HELL of a deal! As it was low (and I always use an appraisal contingency) I was able to significantly lower my out of pocket and buy price. THe seller NEEDED to sell at almost any cost... hours from crunch-time I was ready to walk, so the agents put in a little commission and I ponied up a few thousand. Today this duplex nets me nearly 1500 per month! (and I "overpaid")
Last week I got another "okay" appraisal on a rehab project. While it didnt come out with tons of room for a complete cash-out refi, the relationship i've developed with my team (including my lender) allowed them to figure in the INCOME that my stuff produces.... THey allowed me to borrow more than the appraisal based on comps.
I use them as a sanity check.