Pricing over assessed value isn't an issue because there will be an appraisal (if one hasn't been done already).
As to the rest, it's not the down payment that is an issue. For virtually any type of loan except rehab loans the property does have to meet certain minimum standards. The needed improvements can be minor (CO detector) or major (new roof). Even if the buyer has enough cash to pay for the house without a loan, the bank is not going to make a loan without the house qualifying for the loan.