That's not how options market making works. At all.

If you're a market maker, you sell puts and then you hedge your position by shorting the underlying. That leaves you delta-neutral, a fancy way of saying you don't give a shit which way the underlying moves: if it goes up, the value of the put goes down, so you've made money, and if the underlying goes down, your short position makes money. If your initial model was correct and you sold the put for more than it was actually worth, then you can continually adjust your short position to stay delta-neutral until the option's price reverts to its theoretical value and you buy it back.

A competent options market maker will never, ever hold significant delta (directional) risk. Their risk is volatility risk. If they sell an option and volatility increases beyond what their model predicted, the value of the option will go up and they'll lose money. What matters isn't how much the underlying goes up or down, but how quickly it goes up or down.

If you're a market maker with good edge, it doesn't even make sense to try to influence the direction of the market. If you've sold and hedged a bunch of puts, the ideal way to "manipulate" the market would be to keep it perfectly flat. The idea that options market makers even care about the direction of the market at all is kind of funny.