You could alternatively think that hedge funds don't have enough trading volume to shift the prices so far that the heuristic stops working. Imagine a market composed of a thousand idiots, one hedge fund, and you, each participant having roughly equal resources. If all the idiots make some mistake, the hedge fund will get there before you and profit from it, but unless it's leveraged 1000:1 (which would be ... brave) there are likely still profits for you to take by exploiting the same mistake.

In reality there are a lot of hedge funds and some of them have an awful lot of money, but they're still no more than ~1% of the market.

No because hedge funds would already be doing this, and you would have to think you were better at it than them.

Consider funds that close out their positions by the end of every day. They're implicitly being as fearful as possible (in a world with just cash and stock), which is not obviously the optimal approach to long-run timing.