Having been in and around the auto business for 40 years, here are a few things. ( This is in general and not directed to a specific person.)

Car dealers don't inspect every square inch of a car. Better dealers fix what the car needs to operate but even then they are not going to replace hoses / belts that are still working. A used car is just that, used.

For a PPI I'd use a new car dealer of the same make or at least the same parent company. A shop owned by an established enthusiast club would come in a strong second especially for an obscure / older car.

Customer expectations ( and to some extent IQ ) are proportional to the asking price of the car. As in the lower the price, the higher the expectations and lower IQ of the buyer. When I worked as a tech at a decent used car lot, I could watch someone get out of their car and by the time they got across the lot would have a pretty good read on how they would act. How one carries ones self speaks volumes.

There is a line between adding buzz to an ad and lying. Lying is never acceptable. Private sellers really might not know that there is something wrong with the car so what they say isn't considered reality. Don't mistake someones incompetence for lying, this applies to businesses as well.

Some time ago 2 people on this list made a deal on a car. Both were apparently well meaning but were lacking in skills. The seller apparently talked the car up not knowing that there were issues / didn't think they were critical and the buyer didn't know what to look for. Who was wrong? Both were with a slight tilt to the buyer.

On my end of things, I'm the one buying and make my own decisions as to if the item is as described. I've gotten some pretty good deals when the seller considers a slightly broken item completely junk.