Enterprise Rental Car Enterprise Rent-A-Car wants me to pay for damage to vehicle that i did not do St. Louis, Missouri

I was on my way to work when I heard that the tire pop. To avoid rush hour traffic I moved over the right of the road to check the vehicle. When I got out of the car I saw that the tire was flat. I first contacted Enterprise location by phone which was not open at the time and selected the phone option to contact Roadside Services. Roadside services said there may be a fee of around $60.  Roadside service arrived after I placed a call to Enterprise and made them aware of my situation. The associate advised that he will take care of roadside assistance fee.  The Roadside gentlemen replaced the tire, place the spare on the vehicle and placed the tire and rim in the trunk of the car. I headed back to the office in which an associate gave me a new contract and put me in another vehicle.  I received a call from one of the associates who advised that I hit something and damaged the rim of the vehicle and that he will need to put in an accident report.  So then I asked if he had a report number (which was not available at this time). Then I went online for the phone number to Enterprise Corporate Office and filed a complaint.

That evening I received a call back from the Regional Manager who advised that the situation is cut and dry and from what he was told I am held liable for the damages of the rim. I told him that I was not going to agree on that because, first I dont believe that I caused damaged to the rim from a flat tire and second, I had no idea what cost of the repair of the rim. He then said that to estimate the cost would be around $300-$400 He told me that he would call me back tomorrow.  I contact Enterprise in the morning and spoke with the store manager to ask him the accident report  number and the (phone number of roadside assistance he was not able to provide) and to see if the rim was there for inspection.  So I received another call from the regional manager who stated that he was currently at the body shop and inspected the damaged rim and that it was no way possible that a flat couldve caused that type of damage. He also said that I only had 2 options to come out of pocket and make a payment or that he would file a claim with my insurance company. I asked him the name of the manager he reports to. He said that he was the regional manager of the claims an he has the final say. 

So I contact corporate again the next morning to advise that I was not satisfied with his offer. I feel that because I am woman and dont know much about vehicles that I am begin take advantage of. I also feel that its my word against Enterprise  for the simple fact that rim couldve came from any vehicle and I am made to pay for it. I sat in the office after the incident and no one went outside to inspect the vehicle with me begin present to show me any type of damages made to it. I also feel that since the waived the roadside assistance fee they felt this was probably another way to make their money back. I know that since it is a business  whatever they charge me as the fee for the damages would not be what they paid for but what they would charge the customer for. I feel that my character was defiled and I was basically called a liar even though the associate and the regional manager did not come right out and say it. And now Im looking for other options to resolve this matter.