Actually, you are right, MM's do short. But that is simply their business model. When you place an order for shares, they have to go buy it. That makes it a short, because you don't have your shares yet and they don't want to own it. They are a broker of sorts.
When you DO get your shares, which is almost immediately, the MM is still short because both the buy and the sell take 3 days to settle. The SEC is changing that to 2 days soon, but for now, that is how it works.
MM's do buy shares when a stock isn't moving too...that is what they are there for. To make the market. It's worth googling market makers to learn how they operate. I can assure you that it is far from what most traders think it is.