An appraisal is an Opinion of Value, it is not a statement of absolute fact. Appraisals are done by people, some great and others are out of their area, out of their experience or just wrong. I have disputed appraisals and had adjustments made based on additional information I was able to provide. I've had second appraisals that have come in at the value I was expecting after the first one was low.
The Real Value of anything is generally described as what a willing and able buyer and willing and ready seller agree to do business with. For financing purposes, we have an additional opinion of value through the appraisal process.
It's hard for me to say what broke down in your situation, but as you describe it, multiple offers over list price indicate the demand for this particular house is high. If there are not any recently sold comparables to support it for financing purposes, it will come back to what the buyer's and seller can negotiate from here.