I think there is more to it than all tree not decomposing due to lack of lignin digesting fungus. From what I've read the trees had to have fallen in an area of freshwater only it could not be saltwater or it would rot.
Yes, there are many factors at play environmentally beyond a lignin digesting fungus. Just the whole timeline and that aspect that makes one tree a fossil and another a fossil-fuel, is fascinating and the aspect that there seems like a cross-over period in which some trees of a time became coal and others became other forms of rock (yes coal is a rock, covering myself in case of any lurking coal-ologists :).
Makes you wonder what the planet did look like and maybe one day we will be able to work out were land masses and at what height and climate, that with coal and oil fields, see a picture of the forests that made that coal and oil. Though a quick google didn't jump out anything close.
Then again I'm no coal-ologist.