No, what really happened is exactly the OPPOSITE of what you're describing here. The redditors were using options to pump up the price and the hedge funds were actually shorting, not by using put options but by actually borrowing the stocks.
The only way redditors could push the price so high was by buying call options (which then force the broker to actually buy the stocks). That's how you can push the price higher without having a ton of $$$.
You buy 1 call option - gives you the option to buy 100 stocks at a certain OTM price - then the broker has to buy these stocks to reserve it (in case price goes up and you actually want to exercise the option). So with a small relative investment these redditors caused a high bump in the price as buying 1 call option is much cheaper than actually buying 100 stocks.