They have such an outsized influence on the market? seems farfetched
Its not as farfetched as it may seem. If you believe the short interest reports there are tens of billions of $ on the line if gme gaps up. Hedge funds don't have billions in cash so they would need to sell off a lot of mainstream stocks to cover a MC. And adding billions to the sell side in concentrated sector (eg tech) does tend to have a spiraling effect.
Of course theres plenty of room to disbelieve many of these assumptions. But it could be valid.