I am only now seeing all the answers. As I have not received one after a couple of days, I thought that nobody answered. Anyway, a belated thanks.

I have signed a document without reading it, as I was a little confused. The Sixt guy told me explicitly "that means you deny responsibility, please sign here". But I did not control the paperwork. (Big mistake, I know)

My credit card is a Mastercard World Elite issued by a Mexican bank. I will check with them.