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Why on earth would you assume you could move corn residues with air?From what the article describes later on, it appears the air pressure was actually generated by the tub grinder itself, not by any additional device.
So the appeal of the original design might have been that no active conveyance solutions was needed at all: Because the grinder's air exhaust stream - which you get "for free" - already provides enough pressure to move the material up the pipe, as long as the material is light enough.
That lets you greatly simplify the design, because now you can connect the grinder and the mill with a simple pipe and be done.
For me it makes sense that they used the simplest possible solution that worked for their previous use cases. When trying to use their system with corn, they probably wanted to give their previous approach a try, before taking the time and effort of modifying the system.
Edit: Got it wrong, both grinder and mill were creating the pressure. But the basic point is still correct I think. The choice was not air vs belt, it was "use the airflow that's there anyway" vs "build some active transport in addition to airflow".