This has always been the rule.
Banks will lend "X" % based on the the lower of the sales price or appraised value.
You mention assessed value which implies what the town had assesed the home for, which banks really do not consider where those values are stale dated. I believe you are referring to the banks appraisal which in this case came in lower than what was the agreed to sales price.
Going forward, I'd have your Realtor provide you with recent comparable sales prior to making an offer. Another angle might be to get a copy of the appraisal that was done for this original property and review the work and comparables that the appraiser chose.
I'm happy to talk with you more....