Personally, I wouldn’t throw away my chopping board quite yet. Some granite can scratch less than others because of their density; other granite can scratch quite easily. And by the way, just to be safe, I wouldn’t put direct heat on a bare countertop either. You’re spending good money for your material, so, to be cautious and to protect your investment, using a cutting board and trivets is highly recommended. It’s a good rule of thumb that it’s always better to be safe rather than sorry.