Charged for an existing damage

On Saturday I hired a car for a few hours and before I took off, I advised the gentleman assisting me that the right front tire looked flat to me and he made very lite of it and said a bit of air pumped into it should sort it out. Upon my return another gentleman noticed it and requested that I innocently must state what happened which I did in writing. Only to receive an invoice a few days later with an amount to pay claiming that I have damaged the car. What was stressful besides the surprise that Mohammad denies this taking place, is the fact that the claims department resolves their queries via email and they don't even allow you the courtesy to have an actual conversation with them. So if you are considering using this car hire service I recommend that you do an absolute thoroughly inspection or better yet do not use them at all as in the end you will be made to look untruthful and they protect each other. Even the claims department manager stated what bad condition the tire was in which ultimately means my life was put in danger.