I do that all the time myself and don't worry about it. We do have a much larger hearth than required, so part of the wood is not inside the required clearance range, but of course it is within the 36" that they say not to have anything combustible. I have the wood laying down, so unless there is an earthquake, the wood isn't moving. (No pets or kids or poltergeists here.) It would depend on your stove and how hot it gets around it. Our particular soapstone stove only gets up to 350 F on the top, and we have taken extensive temperature measurements of the nearest wall, under the stove, etc. No other area is nearly as hot as the top, so I would have to say that at the distance the wood is from the stove, and not becoming noticeably hot, there is NO WAY my wood is going to spontaneously combust. Given the trouble of getting a fire going in my stove when there are a few hot coals, I also have little fear of a spark escaping and then setting a slightly damp piece of wood on fire. Also, the stove door is in front and the wood is mainly on the sides and back, so sparks wouldn't tend to go there. I worry a lot more about the couch nearest the stove. Plus, if a piece of wood on top of the tile somehow burned, it would most likely be contained on the non-flammable tile. We do keep an attractive widemouthed vase full of water near the stove all the time, for flinging at sudden sparks if necessary. Only used it once, on the floor in front of the hearth when a small hot bit jumped. Yes, you could come up with a scenario that is dangerous, but probably you are more in danger from eating too much beef or potato chips or something.
I frequently make and can jam, salsa, etc., and I reuse mayo jars and the like all the time. This is not advised, and people are always telling me how this glass will break. I have canned over 500 jars of stuff in the past 3 years (lots before that, too, but that is the only statistic I have.) The only jar that broke was an official canning jar, and that is because I dropped it TWICE. So I let that advice go in one ear and out the other. As long as the wood doesn't sit there for weeks getting really dried out I don't see a problem. Just don't let the wood touch the stove of course. Disclaimer: I am not an expert, and don't play one on TV.
Has anyone ever heard of a house fire from damp wood being dried near the stove?!? I can't imagine it in a case where the wood was not touching the stove directly. This isn't like overloading an electrical circuit or chainsawing without protective gear or something definitely, unarguably dangerous.