Some universities will allow you to purchase your OSHC through them, but it is not a requirement that you do. They will usually have a specific "preferred provider" that they've partnered with and this may give you access to special rates or increased levels of cover that the insurer does not offer to the general public.
If you purchase your insurance through your university, your university may also help organise your first payment to the insurer and advise the Department of Home Affairs on your behalf.
A drawback of going through your university is that there will be lack of choice. Your best bet is to see what they offer and compare it side-by-side with other policies in the market.