Anyway, this release of methane seems speculative and not a good indicator for what could happen with our current release of CO2.
The release of a large amount of methane is the only plausible explanation for the large shift observed in stable carbon and oxygen isotope ratios at the PETM. There are references to publications by Katz (et al.) that might provide an explanation for the cause of the release. It seems clear that the ultimate cause of the methane release is unclear, but it is clear that the methane release followed by oxidation to CO2 is what actually happened.
Anyway, this release of methane seems speculative and not a good indicator for what could happen with our current release of CO2.
Both methane and CO2 are greenhouse gases that change the Earth's radiative balance if their atmospheric concentration changes. Provided that a methane release and oxidation to CO2 is what happened at the PETM (and that's what "fits the facts at hand"), then the PETM shows that greenhouse gas increases in the atmosphere can drive a warming trend.