Advice on buying a home at over its estimated value

As far as I have come to understand, a home's estimated value is based on comparisons to similar homes in terms of sq footage and acreage sold in the same area. The home we love, in our opinion (and certainly in the opinion of its owners) is in MUCH better shape than the homes that its estimate is based on - new plumbing, new roof, amazing landscaping, completely move-in ready, the best "curb appeal" of any comparable home. It is really the gem of the area. The problem is that the current owners need more than what they expect the estimate to be in order to leave. They have put a ton of work into the house in hopes of the market value increasing, but just discovered that the difference is negligible. We also agree that the house is worth more than the estimated value, nut the timing is just not working in either of our favors right now.

Is it in fact the case that a bank will not give a loan for a home over the market value (minus 20% down)?

What are your thoughts on buying a home for above its market value in general? It's obviously impossible to see the future, and although we think this area is on the up and up, we might be shooting ourselves in the foot when we try to resell in 7-10 years...

Any experiences in this realm?