Their point is that nowadays carbon from dead plants and animals generally gets recirculated, but this wasn't always the case. Back before the enzymes to break down lignin and cellulose existed, when trees died the carbon they had extracted from the atmosphere didn't recirculate. And if we hadn't started digging up fossil fuels and burning them, that carbon would have remained buried basically forever. So where the oil comes from does matter.

https://en.wikipedia.org/wiki/Carboniferous#Fungi