What does it mean 'the car is PS title'?
It means that the car was damaged, but was not reported as a salvage title. A PS Title is Pre-Salvage. It is a clean original title on a car that in most cases should have been transferred as a salvage title, but for whatever reason was not.
No, the bottom line is, the title must have the owner's name. Put in reverse situation, if your car was taken by someone who has your title to the car and the car should not be missing, then you would want the car back even without a title. People lose car title all the time, that doesn't mean they lose the car just because they lost the title and someone picked it up.
The title covers ownership of the car. If your name is on the title, then normally you would be considered the owner. If a banks name is on the title, then the bank owns the car. Ownership means the car and all the stuff attached to it. It does not mean you own someone else's property just because they left their property in your car.