Good subject OP. I bought a CPO 2011 Lexus Rx350 in 2014 from a Lexus dealership. I am very happy with it. However I got talked into an extended warranty and have only needed one shock absorber which was covered by warranty. So I think that for instance if you buy a Toyota from a Toyota dealer or Lexus from a Lexus dealer they will sell you a decent vehicle because their reputation rides on it. You probably can get a better deal privately though and a PPI would be recommended. I had a PPI done on the Lexus even though it was a CPO.
Conversely my daughter bought a 2014 Audi Q5 from a Porsche dealer. We had a PPI done and it is a great SUV. If the dealership has a good reputation that really helps. Check the reviews. The more stars the better. ...
Let us know what you decide.