This seems to be misrepresenting the "blindfolded monkeys" thing. Assuming that equity prices are an unbiased random walk, a blindfolded monkey will on average

This seems to be misrepresenting the "blindfolded monkeys" thing. Assuming that equity prices are an unbiased random walk, a blindfolded monkey will on average do exactly as well as anything else. The reason the professional stock picker is a worse choice is they charge you more for their services, and this is where you lose money on choosing them. It seems that unbiased random walk is a fairly good model of short-term equity returns. So no, I don't think "do the inverse of a stockpicker" would on average do any better than just following their advice. Additionally, if the fund charges for their service of maintaining that inverse exposure, it will perform worse in end-user returns.