In the latter case they reported the car as stolen after it had already been returned! Don't worry, that happens. Hertz will not hesitate to call you, saying

In the latter case they reported the car as stolen after it had already been returned! Don't worry, that happens. Hertz will not hesitate to call you, saying that the credit card used for the rental has been maxed out, and could you supply a different credit card. Always keep your receipts.