That sounds intuitive but does not follow. The strength of the random strategy is that it approximates the theoretical ideal - a maximally diversified market-cap weighted portfolio. The non-random strategy is too concentrated, and inverting that can leave you with another strategy that is also too concentrated compared to the ideal.
The problem isn't that the non-random strategy did poorly, it's that it has too much exposure to needless sources of uncertainty. The inverse strategy doesn't get rid of uncertainty, it just flips the sign of their exposure to that uncertainty.
The short answer is that hedge funds etc hire teams of math PhDs, rent out supercomputers, acquire non-public information like satellite imagery, and do various other hard activities in order to accurately price securities. Unless you think you can beat these players at this game, there's no way to pick better-than-average stocks.
The longer explanation is that you can break down the price effect of various real-world events into two axes. There are things that transfer market value between companies, and things that change the value of the market as a whole. For example, people buying more Macs instead of PCs will transfer market value from Microsoft (among others) to Apple. On the other hand, a novel form of efficient energy production will do more to increase overall economic activity.
The maximally market-cap weighted portfolio has diversified away the first axis of risk. Suppose company A, worth $500M, loses $50M of market cap to company B, worth $100M. If you own $500 of company A and $100 of company B, the $50 loss from owning company A stock is completely offset by owning $10 of company B stock. You're purely exposed to changes in the value of the economy as a whole, and have eliminated diversifiable risk from your portfolio.
If you can't benefit from taking on diversifiable risk, you're better off getting the same return at a lower level of risk by simply removing it.
The problem isn't that the non-random strategy did poorly, it's that it has too much exposure to needless sources of uncertainty. The inverse strategy doesn't get rid of uncertainty, it just flips the sign of their exposure to that uncertainty.