Given the wackiness of the housing market, I hesitate to offer my expereince as a former real estate professional and banker but here goes -
What I would often see with FHA loans is a sale price set high enough to cover the seller "paying" the closing costs. Agents knew which houses would great options for first time homebuyers, ones that could pass the extra inspections and were in that first time buyer price range.
For example, a house listed at $80,000 would sell at full price to a FHA buyer and the owner would give back $5,000 for closing costs. A conventional or cash buyer could offer $75,000 and the seller would accept.
This is what happened when we sold our house, the agent recommended that we priced it at a point that we would take full price offer and contribute to closing costs for any buyer requesting assistance with closing costs. The price we needed to sell the house (and would have accepted) was a couple of thousand lower.
The end result is the same, it is just how it is presented on the paperwork.
I mention this because as RE appraiser and later as a banker, I would run up against these types of deals and sometimes there were problems getting comps to show the purchase price in an FHA financing deal was comparable to the market. In fact, the type of financing (or lack of financing if a cash deal) was one of the disclosures required on appraisal forms when presenting comparables.
Conventional loans with downpayments of less than 20% used to require PMI insurance, which was pricey. The percentage may have changed.