So the argument is that finding and chopping a log with a hatchet is less LNT than finding and throwing a big rock, splintering wood everywhere and probably gouging out the ground?
I mean, the OP was asking about firewood. Already he is leaving a trace. (fire) I wasn't suggesting cutting down a tree with a hatchet. They are not made for that. I'm saying is use a saw to cut to length, then hatchet, if you want, to split it.
He's leaving a trace, so LNT shouldn't have come up. But since it did, dragging a big limb through the woods and finding a big rock to bust it up leaves more of a trace than a small saw and a hatchet.
EDIT- as for the high country sites, don't make a fire no matter what (i guess if your life is on the line its ok...)