I looked at the brown spot, and I see the fiber from the glass. I also some osmotic blistering where water has worked it's way through and lifted up your gel coat. I would do the drill shaving test, or if the drill is too risky; scrape with a small 1/2" wood chisel until you hit wood that is not brown and wet. Another test is to put some weight on that area from the inside, and have someone under the boat, or video camera that area while you put force on it. If it bulges out when you step, or press on it, you have you answer. Take out the rot, add new stringers, floor, and transom.
