The methane and CO2 produced are "current account" carbon sources, ie, carbon that was in plants that are decomposing. It's not ideal but it's relatively neutral as far as heat effects.
It's similar with cow farts. They eat grass, metabolize it, releasing gas as a by-product, which eventually is taken up by vegetation and re-sequestered.
Anthropomorphic warming is due to digging up and burning geologically sequestered sources of carbon like coal, oil and natural gas. By doing so we're injecting millions of years worth of sequestered carbon annually. Natural systems can't process it fast enough, so the atmospheric CO2 level has been increasing.
