No Doc loans are pretty much a thing of the past.
Your friends situation is typical for short sales. Most of the time the bank does not set the listed price of these short sale homes, the owner and their agent dream up these prices to promote offers. They then "HOPE" the bank accepts it or counters it with something close, but as your friend has seen they sometimes come back with what they want and it might not be close to what the owner has dreamed up.
Banks will let it go to foreclosure, they won't think twice about it and you need to understand that banks are not like you and me with our money involved. They would often rather let the house be foreclosed and get the owner out of the picture and then they can sell it as a bank owned home at the current value of the market. Reasoning with them about taking this rather than letting it go to foreclosure is a waste of time, banks don't think like that very often and they have procedures they follow and they are not always rational ones you or I would do. Love those short sales.