@Amie2018here I don't think universities have access to immigration information aside from VEVO (if visa was granted); only DIBP (immigration) can see his prior visa applications.
Since school yung nagreject ng application nya, focus muna kayo na ma-approve yung school application before worrying about DIBP. As long as complete and legit naman yung application nya for a student visa, there's no reason for DIBP to reject his student visa application.
If your cousin doesn't mind, can I read through his SOP? Para may idea ako kung ano yung ipinasa nya sa school. Or may iba pa bang feedback yung school regarding his application aside from the SOP?