While your current personal coverage will probably cover you, there are several things to consider.
Your agreement with the rental company is contractural. In some rental contracts you may be agreeing to pay for things that would not be covered under your insurance. Some examples: You may be agreeing to pay for the loss of use of the car while it is being repaired. So if you have an accident and it takes 2 weeks to repair, you will probably be paying the daily rental rate during that time. ( many insurance companies offer this as a buy back, but you have to ask for it . The latest item to show up in rental contracts is diminshed value. You rent a car, have an accident and several months later, you get a bill from the rental company for several thousand dollars because when the rental company went to sell the car, the value was diminshed because of your accident.
There are other things to consider. You only have older cars and do not have coverage on the cars anymore... YOU DO NOT have coverage on the car. YOur Visa or Mastercard may not respond because it is normally excess of your coverage. Your accident is in Orlando and you live in New Jersey. You have an accident and you have to call your agent at home and they are trying to handle the claim from 800 miles away. Not an easy task. Sometimes the rental company will fix the car before the adjuster gets there. Remember the contract is with you, not your insurance company. The adjuster does not agree with what was done...
The bottom line is most people say they are covered through their insurance and or credit card. Probably, maybe, I do not know for sure....