The problem with buying a vehicle from a private party is that there aren't very many available today - at least if you are looking for a late-model vehicle that is 3-5 years old. The VAST majority of those cars are lease returns or a trade-in from someone that buys a new car every few years.
You can find old used cars for sale but I have zero confidence the owner will have records to show me the maintenance has been done. Someone that is going to go through the hassle of selling a car themselves is also someone that is likely to do their own maintenance - or skip the maintenance. Someone like Redpoint