Medical coverage when renting a car.

We purchase our own travel insurance with medical coverage
The cost is really not much- buys us peace of mind and if we had to be medically evacuated we are covered ( that could be a HUGE expense)
Since your Medicare will not cover you, you really should consider it

Use insuremytrip.com to compare policies/rates

I'm not aware of medical insurance attached to any car rental. The rental includes liability insurance. You can also buy collision insurance for the car. But you need to buy your own medical insurance for the period of your travel.

It's not only the car . If you should sustain a health care condition ( an accident , a fall that causes major injury , a cardiac event , as examples ) you would need major medical intervention and perhaps , evacuation of some distance . Walking about uninsured anywhere would be foolhardy . Absolutely , purchase insurance .

If you have an AmEx card, check on buying your Medical insurance including Medical evacuation from them. It's not expensive.

It would make more sense to purchase medical coverage for the trip not tied to auto accidents.

Auto rental medical coverage is very specific in that it will cover only injury sustained while in the rental car. So if you purchase the medical option for your car rental then fall down the stairs at your B&B lodging and break a hip, you would be on your own to pay for it. Most travel insurance plans contain medical coverage and it is not overly expensive.

There are numerous travel insurance companies you should consider to cover trip costs and medical emergencies.
Allianz, Travelex, Travel Guard are 3 that generally rank among the top best.
They are not expensive, and what drives the premium is the total trip cost that you state in the form and is the basis for reimbursement in case of cancellation or delay, which are the most common reason for people filing insurance claims,
The medical coverage part is not really expensive at all as medical emergencies claims tend to be rarer events.