Bud, some DMs are hilariously bad at hiding their behind the scene work.Infinite, because yes, the DM has infinite reserves if they want to use it. It is a fine use of hyperbole. If you sat at their table, I doubt you'd recognize any use of "infinite" in their game. You are taking things too literal.
My cousin's best friend is a DM and terrible at it. His table has a notetaker, an exploiter, and an optimizer.
Queue the ensuing hilarity.