I've been following The Great War on YouTube and this pops up now and then, and I'm genuinely curious if this was a real thing or an overblown fear of certain German generals, disregarding other Russian inadequacies in armament and industry.
The german war plan (Schlieffenplan) was dependent on Germany defeating France fast and then turning towards Russia. Therefore, the speed at which the russian Army could mobilise and be brought to bear did matter in the pre-war planning. France did grant extensive credits to Russia before the war with the stipulation that the rail network be upgraded to allow a faster mobilisation.
So, the russian rail network was seen as having importance to the Schlieffenplan by both Germany and France. Was it seen as a decisive factor? Probably not. There was a general sense of urgency in Germany in August 1914 (better war now than later), but this was linked to the strength of Russia in general and not to the state of the rail network in particular.