That theory is not really disproven, even if it was not the only reason for the huge accumulations of coal during the Carboniferous.

Coal has been always forming later, even today, but never in such quantities, because later it required much luckier conditions for the wood to not be decomposed by fungi.

The climate and the position of the continents during the Carboniferous must have contributed to the accumulation of coal, i.e. it is likely that a much greater percentage of the surface of the Earth was covered by some kind of swamps with warm climate, where plants were abundant and dead wood could submerge and be protected from decomposition, but this still does not appear to be able to explain the so great discrepancy in the amount of accumulated coal.

The most likely explanation is that all factors must have contributed, the conformation of the continents, the climate and the low abundance or absence of wood-digesting fungi, or perhaps there already were wood-digesting fungi, but their enzymes were not as efficient yet as those of later fungi, so they could decompose only a small part of the wood before it was buried in sediments.