You can artificially tie together those two things and call it "carbon-neutral", sure. And you could also plant trees after burning coal (let's say on a small scale) or running your car and claim that coal and gasoline are carbon-neutral as well.
There's nothing artificial about it. If x tons of carbon is locked up in a managed forest, and you burn and plant wood from that forest at such a rate than x tons of carbon continues to be locked up in that forest, then that usage is, both by definition and absolute and incontrovertible weight of fact, carbon neutral. That's what the term means; no net change in the amount of carbon released.
And yes, you could do the same with coal and oil, as long as the trees you plant are new growth, are never cut down, and never counted against any other carbon usage; that is the whole concept of "offsetting". However that is much harder to keep track of, and in my opinion not a great idea.
This is missing the point. We're almost certainly not going to be able to grow enough trees or other plants fast enough to recapture all of the carbon we release through all of our hydrocarbon combustion.
Nobody argued otherwise. The fact that wood burning can't practically be carbon neutral on a massive scale doesn't stop it from being carbon neutral on a smaller scale.
What else would they have done with that wood? To get a proper accounting, you have to compare this to the counterfactual situation where there is no wood burning.
Again, neutral means neutral; no net change in the amount of carbon. Sure, you could potentially do even better than neutral, if the wood is used in such a way that its carbon never ends up being released into the atmosphere, but that doesn't stop neutral from being a good thing to aim at. Solar power and wind power are only carbon neutral; they aren't scrubbing any carbon out of the atmosphere, they just aren't adding any. So sustainable wood burning is on a par with solar and wind power in carbon terms, and I think it's a bit fatuous to complain that that's not good enough.