There are banks that allow some seller carry situations, or if it is a family member gifts of equity. In those situations you would make the purchase price for the appraised value and the seller would carry the other percentage or credit it. Your best bet talk to a mortgage broker, and experienced realtor that have done deals like this before.
Also the reason why banks don't see the equity as down payment is due the fact that they like to see that you have some vested interest in the property. It is easier to qualify when you are actually putting something down or into the property. It is harder to walk away from something you have actually put into and not something you were given. The bank doesn't want people to walk away from there loans and let them foreclose.