The coupled chemistry of methane, carbon monoxide (CO), and hydroxyl radical (OH) can modulate methane's 9-year lifetime. This is often ignored in methane flux inversions, and the impacts of neglecting interactive chemistry have not been quantified. Using a coupled-chemistry box model, we show that neglecting the effect of methane source perturbation on [OH] can lead to a 25% bias in estimating abrupt changes in methane sources after only 10 years. Further, large CO emissions, such as from biomass burning, can increase methane concentrations by extending the methane lifetime through impacts on [OH]. Finally, we quantify the biases of including (or excluding) coupled chemistry in the context of recent methane and CO trends. Decreasing CO concentrations, beginning in the 2000's, have notable impacts on methane flux inversions. Given these nonnegligible errors, decadal methane emissions inversions should incorporate chemical feedbacks for more robust methane trend analyses and source attributions. Plain Language Summary Methane inversion studies commonly assume that atmospheric methane has a 9-year lifetime, but the decay rate of methane perturbations can be extended by 40%. This effect is from interactions of other atmospheric compounds with methane's main sink, the hydroxyl radical. This is important for estimating global emissions over recent decades. We show that one of these compounds, carbon monoxide (CO), emitted from wildfires during El Niño, can lead to large increases in methane concentrations by extending the methane lifetime. Moreover, ignoring these effects can lead up to a 25% error in estimating methane emissions changes after a decade. Finally, we show that the effect of decreasing CO on methane has reduced the methane lifetime and has led to potential biases in calculating methane emissions. Thus, attributing causes of recent methane emissions trends are dependent on the consideration of compounds indirectly affecting the methane lifetime, which may have implications for future mitigation plans.