It is being stated in recent literature that greedy policies provide optimal scheduling for identical scalar Gauss-Markov systems. Here, the performance index is the sum of the covariances of the systems from time 1 to a time horizon. The scheduling decisions from time 0 to N - 1 constitute the policy. In this note we show that when N = 1, the statement is true. Our main result is to show that when N = 2 the greedy policy fails to be optimal for identical scalar Gauss-Markov systems, in contradiction to the statement, and illustrating the complexity of the problem.