Credit Card Payment Dates - impossible timeline

DISCLAIMER: There's no way for us to know what actually happened, and I suspect you have a less than knowledgeable customer service rep, but this is my most plausible explanation.

When you rent a car, the car company typically authorizes the charge and places a "hold" on your card in the amount of the known rental charge plus a deposit for potential damage, fuel costs, etc. That hold just reduces your available credit to make sure you have enough credit to make the rental and to make sure the vendor gets their payment.

So it seems most likely that the hold was placed on the 10th, and then amended and processed once the actual total charge was known. The statement is reflecting the date on which the hold was placed and not the date when it was finalized.