I'm fairly sure - but again, please correct me if I'm wrong - that what actually makes market makers increase or decrease the move of the market is gamma, not OI in either puts or calls - ie. whether MMs have to hedge puts or calls, the magnitude of their dynamic hedging is about the same in either direction.
The MMs already bought the shares to do the initial delta hedging.
Consider this:
What happens if the SP goes down by $5? The delta of all every call they're short is lower, so they have to sell some shares to remain delta neutral. Further, the puts now have a bigger negative delta, which has the same effect, they have to sell shares.
What happens if the SP goes *up* by $5? More or less the same thing, but in reverse. The call delta is higher so they need to buy more share, the put delta is less negative so they have to buy more shares.
This is the effect of the MMs being short gamma - they will amplify price movements by dynamically hedging. If they had long gamma (ie. people wrote options instead of buying them), which basically only happens in indices and ETNs and volatility products and such, they would instead have to do the opposite and would thus dampen the price movement.