I love this story and have repeated it to many people because of how wonderfully it sparks the imagination. Unfortunately, this theory simply doesn't hold up to modern evidence. It turns out we've had white rot fungi as long as we've had lignin
> Throughout the fossil record, evidence of decay is pervasive in all organic matter exposed subaerially during deposition, and high coal accumulation rates have continued to the present wherever environmental conditions permit.
> Rather than a consequence of a temporal decoupling of evolutionary innovations between fungi and plants, Paleozoic coal abundance was likely the result of a unique combination of everwet tropical conditions and extensive depositional systems during the assembly of Pangea.
Wood and other plant matter is still turning into peat under the right circumstances to this day. And peat is still slowly turning into various kinds of coal. It's true that the majority of coal (about 90%) originates from the carboniferous period, but microorganisms today does still not manage to break down all cellulose under all circumstances.
The Paleozoic peak in coal deposition was not due to white rot fungi evolution lagging behind lignin evolution. In fact we have plenty of evidence that fungi were pretty much always able to decompose lignin
> Here, we demonstrate that lignin was of secondary importance in many floras and that shifts in lignin abundance had no obvious impact on coal formation. Evidence for lignin degradation—including fungal—was ubiquitous, and absence of lignin decay would have profoundly disrupted the carbon cycle. Instead, coal accumulation patterns implicate a unique combination of climate and tectonics during Pangea formation.
Curiously near Chernobyl, decomposition microbes are suppressed, so things can hang around longer: https://www.smithsonianmag.com/science-nature/forests-around...