The Nash-Equilibrium solution to RPS is playing each option a third of the time. Simplified, this means that if you're playing this strategy, your opponent's best strategy is to do the same and there is nothing either of you can do to increase your own expectation.
This thread is talking about playing random -- by aid of a computer providing random numbers. The result is just that -- 1/3 of the time each option is played. The issue here is this AI is able to best random, and that is not something that should happen.