Let's make sure we're talking about the same thing here. CDW is a fee (sometimes covered by your credit card) to pay for any damages to the car. There is usually a deductible as well, and they will likely put a hold on your Visa for that amount, which could be $1000 or more. You can opt to take "Super CDW", bringing the deductible down to zero....but that is usually NOT covered by your credit card, and may not be offered if you decline the rental firm's CDW to use your credit card coverage instead.
Liability insurance coverage, to pay someone who may sue you for injuries or damage in an accident, is usually part of your rental agreement...check with your rental firm to see how much they offer ($1 million seems to be the standard these days.)
As for the Visa provision that doesn't cover people inside the vehicle...that sounds a little odd. Any passenger who, for example, was hurt in a car accident could go after you as a third party. I would definitely check with Visa about this.
As for your health coverage...again, Access America may only cover ACCIDENTS....not illnesses...and that leaves a gaping hole in your insurance coverage. And I'm not sure I would travel with just $10,000 for medical bills.
Personally, I ignore credit card CDW coverage since I like taking the Super CDW to reduce my exposure to Zero dollars. And I can never seem to get a straight answer from them as to what it covers and what it doesn't....at least it's all spelled out in your rental agreement.
And as for health insurance, I make sure I'm covered for EVERY eventuality...for the relatively small cost, it gives me peace of mind.