So if I am understanding this correctly, the MM is essentially hedging all calls/puts, irrelevant of whether the option was opened as covered or naked? Sorry if I am misunderstanding, still trying to grasp it all.
Yeah. The MMer sees it as a single; a short call. He lays it off (covers it) (or) buys half shares (straddle conversion) or some other hedge to flatten his delta.
Regardless of whether it's a synthetic short put or he only sees the short call; the only difference is buying or selling the shares.