NICNET (http://www.nic.in) has long been used in India for government mails and official data. You literally have dedicated VSAT connections etc. to it in offices, and it is a separate network in itself.
The Indian army too for obvious reasons, just like its counterparts everywhere, maintains its own nationwide network, and does not allows internet connections to it.
All they are asking is, that officials use these network, which are NOT public, instead of allowing the data to pass over any backbone that US has control over. And thus no classified data is expected to ever hit any backbone that is in US control.