Yeah the snippet of the wikipedia page that you link is citing the paper that put the final blow to the fungal lignin breakdown hypothesis. It points out (the last point is particularly strong):

* there is evidence for partial lignin breakdown in existing deposits, so we know it was a thing back then

* if it were just lignin breakdown, then we'd see orders of magnitude more deposits. that is, if you look at the per year deposit rate, you'll see only a small fraction of lignin being deposited.

* a large fraction of deposits doesn't even contain lignin, often below or above deposits with lignin, but without there being a different rate of depositions between them.

(copying my earlier comment https://news.ycombinator.com/item?id=34654837 )