Also avoid tiny rental car companies for this same reason. You'll find them listed on the major travel booking websites and they'll have names that you've never heard of. They often appear to be cheaper than the large rental companies, but they frequently have a chipped windshield or a tiny dent in a body panel.
Even if you point it out during the pre-rental walkaround, they won't mark it on the contract. That's the scam. Then when you return they charge you for a new windshield or a body panel/paint job, which of course they never actual have done because they want to scam the next person too.
Yes, you rented your car with your VISA and VISA will cover these charges eventually (takes about 3 months and you're on the hook for the charge for that time, and you'll never get the hours back that you spend sorting it all out).
You could say that you could just make sure all damage is marked before you sign the contract, and that's good advice at any rental agency, but it's still better to pay a little more up front to one of the major car rental companies who make their money on actually renting you a car instead of the company trying to find a way to scam you out of an additional $1000+.