Sounds right to me. It's steep rough terrain. He's one lucky kid and his parents are very fortunate of the outcome.
When I was about 13 years old I hiked with my dad and a friend into a remote area of the Smokies to trout fish. This was in 1969 or 70 I think. We hadn't seen the morning paper when we started out and we were greeted by Rangers and National Guards. It seems a 8-10 year old boy named Dennis Martin got lost the day before. He was never found despite a massive search lasting several weeks. That night and the next it poured down rain. He could have been lying 5 feet off the trail and 50 people could have walked past and not seen him.
A few years back I again I hiked the same trail up to an area called Spence Field. I was coming back down late in the afternoon and was nearing the parking area when I saw a woman running toward me in a panic. She asked me if I had up to the top I said yes. She asked if I saw two boys up there. I said no and asked how old they were. She said something like 8 & 10. I bit my tongue and said stay put while I get the rangers another man was coming by on horse back and he headed up the trail to look for them. I suspect they went to the wrong field by taking a wrong trail. The hike is 10 miles round trip and has several forks in the trail that can take you miles from where you're headed. She was a lucky mom.
The Appalachians are no place to let your kids go exploring alone. They can be very unforgiving in any season. Searches are difficult due to terrain and dense foliage especially in spring, summer, and fall. Honestly anyone hiking in there should take at least a light pack with a change of clothes, poncho, disposable lighter, plenty of food such as candy bars, peppermint etc, and plenty of water. Don't drink form the streams unless you find a spring head. Otherwise consider the water contaminated.
Also take about 30 feet of good strong string capable of holding the pack up. If you get lost and need to stay put then you need to secure the pack by hanging it from a tree limb so the bears don't steal it.
It's fairly easy to lose someone in our forests, and our vegetation is MUCH less dense than yours.