If Hertz can't handle a simple rental transaction correctly without calling the police and resulting in a false arrest, I'm certainly not going to trust them to handle a car sale correctly.
The big difference is that with a sale there is paperwork filed with the state showing that the car is yours. If Hertz gets confused and still reports the car stolen that shoukd clear things up with police and prosecutors.
If Hertz botches it so badly that the state paperwork cannot be correctly filed you will find that out shortly after buying the car and can get it corrected.
