I heard they didn't have very good gear, but it seems they would have fire. I'm in Georgia and there's LOTS of rain in the last few months.
I've been in Derrick Knob several times, where those four guys were. about 11-12 miles from a car parking..., about 5-6 miles south of Silers shelter.
Derrick has water, and both Derrick and Silers shelters were rock walls with fireplaces, but there's almost no dead wood. And even if you found some wood, the "fireplace" aren't made well.
Wind goes right through the shelter, too.
I dunno about stoves, though. They were less than half way through Smokey Mountains..., they should have had "butane" for their stoves.