There’s direct fossil evidence of fungal rot during the period, and that much lignin production without corresponding decay would have sucked all the CO2 out of the atmosphere in a few million years.
Equation of line has nothing to do with reaching 200ppm, as that is average - adapted to whole timeline. Would look completely different in a different scope.
The study addresses CO2 levels closely, as well as other significant pieces of evidence. I would tend to assume the peer reviewers at one of the world’s most prestigious journals thought to Google up historical CO2 levels.