I have to disagree with the prevailing notion that wet wood makes it exceedingly difficult to start a fire or keep it going. I will qualify my remarks in that my experience may only apply to my own local environment. The key is a little bit of understanding and some practice.

First, don't confuse wet wood with green wood or rotten wood - neither of these will burn very well. But wood that has been dead for a while will usually burn without much fuss no matter how much it has been raining or snowing in the past few days, especially if it was still standing rather than laying on the ground. Even then, its not a big deal as long as its not rotten.

Now, in the Kim's case, it looks like the area was covered with evergreen trees. Pine pitch scraped off a tree trunk is 100% waterproof and makes great tinder. Dead pine needles are very water resistant and make good tinder, producing furnace-like heat when you blow on them.

Now find a smallish dead fallen tree (or a standing one who's roots are rotten enough that you can push it over). Drag it over to your firesite and start at the top. When you've stripped and burned everything that is small enough to break by hand, lay the trunk across the fire. When the end burns off, throw the remaining piece on the fire and slide the trunk over and repeat the process. This is a much easier way to keep a fire going long-term than chopping or sawing.

The only reason I can imagine ever using batoning to split wood is if I need a flat piece of wood for some reason.