"A moon or planet would ot be "born" with methane. It has to come from somewhere."
From the context, it's clear what you mean. Methane is a primordial gas found in the solar nebula (note section D). It is trapped within planets, in this case icy moons, as they're formed. Methane has no problem staying locked in water ice until it melts in what I think you know is called methane hydrate.
Sorry Bob, you're mistaken here....