You and michael_dorfman are probably talking past each other, on account of being from different countries with different "Medicare" systems. The US, Australia and Canada all have systems called "Medicare".

In the US, Medicare is only for old people, and it's uncommon for them to attend university. Also, "uni" isn't a usual American colloquialism. So it appears that michael_dorfman is talking about US Medicare, and you're probably talking about Australian Medicare.