I had the exact same thing happen to me with a rental car in France. And you are right, now that the charge has been charged back to the rental company, they can not come after you for the money. You can call them, or better yet, send a letter stating you are no longer liable for this money as you have the paperwork showing the car was undamaged when you turned it in and that the credit card company agreed with you by reversing the charges. They should therefore cease and desist these harassing, even illegal, letters. You can find lots of example cease and desist letters on the web as a guide.
When I was involved with this situation in France, I told them that any damage they claimed to have found on my car must've been done AFTER I had already dropped off and had my car inspected. The car rental place was at the busy port in Calais, so it was entirely possible. I wasn't worried in the least when I received a letter from them claiming I still owed the money. Were they nuts? Even though I had paperwork saying the car was fine, and I had the charges reversed from my credit card company, they
still thought I would pay them? Whatever
I sent them a cease and desist letter and left it at that. I never heard another word from them. I don't think it was because my letter threatened them or anything, but rather, they knew they were dealing with someone who could not be scared into paying money they knew perfectly well I didn't owe.
And let's face it, this isn't a criminal case, it's a simple payment dispute. It's not going to follow you into another country or anything like that. I'm pretty sure that it could only follow you if you were resident in another EU country. Since you say you are not, then don't worry about it. Even if you were resident in the EU, they'd be foolish to bring a case against you. You have all the evidence on your side. The most important evidence of all is from their own company stating the car is fine! Anyway, I really doubt they'd take it that far. Also, they do not have access to your US credit report - they don't have your social security number - so don't worry about that either.
Just remembering that whole car rental incident in France still gets my blood boiling. I swear it's a conspiracy or something against so called "rich" Americans.