It ignores the "clustering" effect, which is axiomatic behavior of all random systems. IOW, to be a random system, the RNG has to deviate from average SOME of the time. An RNG that produces output that looks like 1,0,1,0,1,0,1,0,..... produces the predicted frequency of 1's and 0's, but is surely not random.
the paragraph said "nearly flat line". There are millions of these being spit out; I'm sure the clustering effect is accounted for just fine.