Certain company's agreements provide a deductible.
Like for example, USAA has an agreement with Avis, that there customers are only responsible for the first $5,000 dollars in damage and then USAA will pick up the rest(they also include some liability, but I'm not sure of the limits as of now).
So it looks like what ever discount code you used on your rental covers you after the first $6,000(your responsibility).