After noticing a comment on the site, I checked the "Disclaimer" pages on the 2 official sites (Both don't allow storing this data in any form). However, the 3rd source http://indiarailinfo.com/ is not affiliated to the gov.

Are there any NGO/organizations that could push for such data to be made public in India? I'll try getting in touch with CIS (http://www.cis-india.org/).

Disclaimers on: http://www.indianrail.gov.in/disclaimer.html & http://trainenquiry.com/StaticContent/disclaim.aspx