I have kindled quite a few fires in rather wet conditions - in China, Korea, Japan, Alaska, and several western states other than California. The thing in really soggy conditions is to plan ahead and gather and keep your tinder dry. Once our fire was going, we could always dry damp firewood without problems.
Better yet, as I eventually learned, is obtain and use a stove and the appropriate fuel. Dependable stoves can be obtained at a coast ranging from zero (recycled pop/food cans) to units costing over $100. Even packing a stove and fuel, I make sure I have the means to kindle a traditional fire should the stove go belly up. A fire can be absolutely critical to survival, as well as to that nice cup of tea that makes life worth living..
I can only think of a few "front country" type campgrounds where there are prohibitions against taking dead wood from trees - think Yosemite Valley. Imagine the stink that batoning would raise in that kind of environment! I am fairly sure of the regs here - I was a "smokie" (National Park Service) for over forty years. In any case, given a reasonably valid survival situation, Smokie tends to look the other way
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Geezer in Chief