Neighbors wife called me last winter. She was 7 months pregnant and said that her house was filling with smoke for some reason. I went over and she had the windows open to vent and it was 20 degrees out. They had an insert that sits on the hearth. They had stacked wood up against the side. for some reason. by opening the windows she increased the draft as the wood stacked up against the side began to smolder. This increased the fire in the insert and fed the smoldering wood. I couldn't believe that someone would do that. I put on my leather gloves and carried the smoldering stuff outside. what a mess.
Maybe not on the side like that, but I did once set fire to three decent sized splits of very wet red oak up on top of 4" thick steel blocks that were set on top of my old box stove. I put two side by side and one on top to try to trap the heat. Boy, did it ever! I ran upstairs to grab the phone and forgot about it. Lesson learned, and lived to tell about it here. It didn't take more than a half an hour. And I'm not talking about smoldering, I mean an lively, active, flaming fire... right up there on my stove. Makes you wonder why it's so hard to get it going when it's inside the stove.
FWIW the smoke alarm never went off, in spite of clouds of smoke rolling up the basement stairs.
Clearances are to be maintained. Period. Don't second guess your stove, it can kill you. Besides, there is no real advantage to putting wood that close to the stove, the entire room that the stove is in will have basically the same low relative humidity because of convection currents. Low RH is what dries the wood indoors, not radiant heat. During my indoor wood drying experiment last year, my 10 1/2 pound sample split of black birch sat the whole time on my old produce scale about 5 feet away from the stove. It dried down from 57% MC to under 20% in three weeks, without even a fan blowing on it, just natural convection currents in the room.