Well they can buy puts without margin accounts, since those have a cap on the losses, which would also get more valuable if the stock price decreases. While technically a side bet, the options sellers often want to remain neutral in their risk with respect to movements of the underlying stocks, so buying options may influence stock price as well because of the downstream effects the options seller may undertake.

The expanded leverage of short term calls, though not directly buying the stock, may have been one thing that helped explode the GameStop share prices, as options sellers had to buy more shares to limit the losses on calls they had sold as the price increased (a gamma squeeze).