That's a cute story, but the evidence is lacking.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4780611/

The Carboniferous−Permian marks the greatest coal-forming interval in Earth’s history, contributing to glaciation and uniquely high oxygen concentrations at the time and fueling the modern Industrial Revolution. This peak in coal deposition is frequently attributed to an evolutionary lag between plant synthesis of the recalcitrant biopolymer lignin and fungal capacities for lignin degradation, resulting in massive accumulation of plant debris. 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.

from another article: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4780642/

There is a long-invoked but incorrect (9) perception that lycopsid-dominated forests were the main source vegetation of Carboniferous coals because of the abundance and resistance to decomposition of lycopsid periderm (bark) (e.g., refs. 1, 4, and 5). Thus, lycopsid dominance supposedly was essential for formation of the economically important Carboniferous coals. In what initially appears to support this perception, Nelsen et al. (8) use spatiotemporal trends in Phanerozoic organic-rich terrestrial sediments to demonstrate peak North American coal production during intervals when lycopsids dominated Euramerican tropical forests. Most dominant Carboniferous wetland plants, however, produced little wood, and the arborescent lycopsids were no exception (10). The towering lycopsid stature was made possible by unlignified periderm rather than lignin-rich wood. Therefore, they contributed less lignin to peat accumulations than woody plants, which were episodically abundant, although rarely dominant, in Pennsylvanian–early Permian tropical lowland basins (9, 11). Nelsen et al.’s (8) scientific twist to the hypothesized lycopsid–lignin–coal linkage—that is, documenting coincidence in peak coal production and lycopsid dominance, when lignin would have contributed minimally to peat accumulation—weakens the argument that the emergence of lignin synthesis was one criteria for intensified terrestrial organic carbon sequestration in the Carboniferous.

Large-scale peat accumulation further requires suppression of organic matter decay, of which woody tissue, in the absence of efficient lignin-degrading fungi, has been considered the source (5). Nelsen et al. (8) challenge this view by documenting fungal and bacterial degradation of Paleozoic lignified tissues and, conversely, evidence for abundant unlignified organic matter in many peats. Nelson et al.’s study, building on decades of paleobotanical research, thus unequivocally demonstrates that pre-Permian lignin resistance to decay, and thus preferential biochemical composition of vegetation, was not the key to high rates of peat accumulation 325–300 Myr ago. Intriguingly, lignin’s legacy in Carboniferous peat accumulation may be moot: Nelsen et al. (8) point out that the evolution of Agaricomycetes fungi, based on reassessment of phylogenomic evidence (7), is permissible as far back as the Devonian (420–359 Myr), thus potentially closing the evolutionary lignin–fungal gap. If correct, then a closer temporal association between the onset of lignin biosynthesis and the evolution of lignin-degrading fungi suggests rapid evolutionary innovation in response to a novel resource. Nelsen et al.’s collective findings (8) further resolve a mass balance conundrum regarding the Carboniferous–Permian atmosphere. In a world with hypothesized abundant lignin, the absence of fungal-mediated degradation, in concert with widespread peat accumulation and burial, would have depleted atmospheric CO2 within a fraction of the proposed ∼120 Myr evolutionary gap. Large-magnitude CO2 degassing from volcanism, for which there is no clear evidence, would be needed to maintain the requisite long-term balance in total CO2 inputs and outputs to and from the atmosphere (1).