Auto Insurance Claims: Loss of use, rental car companies, fleet utilization

Question
Hi,
I rented a car from Thrifty in New York City, I do not have auto insurance but paid with American Express, using them as my insurance agent.  The next day in Maryland, I was involved in a 45 mph collision, both parties were fine, but the cars were too damaged to be driven away from the scene and were towed away.  An hour after the accident, I called Thrifty to report the accident and the location of where the car was towed.  Right after my accident with Thrifty, I then called American Express to give them the details of the accident.  Amex Insurance and Thrifty worked out the insurance claim for the car, however, I still have an ongoing dispute with Thrifty.  I rented the car on a Friday and the accident happened the next day on a Saturday.  Thrifty picked up the the car on a Tuesday, even though they had known where the car was for the previous couple of days.  I had originally specified that I wanted to rent the car until Sunday night and have paid for the weekend time.  Thrifty is charging me in addition, two extra days since they picked the car up on a Tuesday and two late fees, one for each day the car was late. In addition, they are charging me a $300 drop fee for not returning the car to the same location.  Is Thrifty, able to charge me these two extra days and a drop fee even though they knew where the car was held.  I assumed that this was be covered under loss of use which Amex does cover.  However, Amex has said this case has been concluded and will not open it up.  Also, Thrifty never provided a fleet utilization log or asked for Loss of Use on the insurance claim.  Do I have any recourse or do I have to pay Thrifty.  
Thank you for your help.

Answer
Hi Peter,

Rental car companies are notorious for trying to charge all kinds of fees when one of their cars is in a collision. They can ask for just about anything. All of it is negotiable. You should write back to them stating what you are willing to pay and what you are not willing to pay. They will make all kinds of noise about law suits and such but you just have to stand firm. Once you reach an agreement, be sure all the terms are in writing before you pay anything.

I hope this helps
Richard Hixenbaugh