That's a bit of a vacuous statement. Stationarity makes sample statistics meaningful due to the LLN, sure, but almost nothing is stationary (and even if something is, there is no way to know anyway, you can only assume). If you condition on enough variables and do enough transformations you may get something seemingly stationary and therefore trivially predictable. But all the practical complexity is in that structure you need to specify. The true prediction "problem", when people work on such "problems", really is in the stuff besides the thing that you can just use averages to predict.