I can't, nor can anyone else here, speak for your credit card's policies. Call them and ask.
I can tell you that your auto policy from the USA won't cover a car in another country though.
Don't just get liability coverage, get collision and comprehensive coverage too--unless you don't mind paying for the damage to the rental car. Total it and you could be looking at a $25,000 bill. That'd make the insurance look pretty affordable.