The problem was less that we had to replace it and more that it was a fairly significant distance away. (A distance made longer because we weren’t on the freeway but heavily trafficked roads in a tourist-heavy area.) We were near downtown Gatlinburg, and there were places that were closer, but they were all closed because it was a Sunday.
We also would have had a better shot at not having our tire blow out if the closest gas station wasn’t 10 miles away.