I have two degrees as well. I'm aware of rugby league at both of those unis and they(RL clubs) are hardly the establishment! Wonder why? I should have qualified my statement with the exception of Catholic(Irish) secondary private schools.
And I'm absolutely certain that more secondary private schools play/allow union to be played as opposed to league. Have you heard of Knox, Grammar, Joeys, Kings....etc? You are surely joking! I note you are labeling union as "Rugby" which shows your real colours. Once again, another RU type dude aiming to deflect the very real issue of widespread bigotry within the majority of the RU influenced private schools. It's pretty logical what we are discussing and you have once again provided a perfect example of a RU type attempt to deflect and misinform for the sake of destabilising this very tell tale discourse its rightful positive momentum. I was school 'footy' captain and 'footy' was rugby league back then and I played union as well. This was a public secondary school.
Arts degrees don't count. Nor combined.
In regards to private schools that play Rugby. They are as follows;
GPS ( 6 schools) Kings, Joeys, Iggies, Scots, Shore and Newington.
CAS ( 6 schools) Knox, Barker, Cranbrook, Trinity, Waverley and St Aloyisus.
ISA ( 12 schools over two divisions) Auggies, Kinross, Stannies, St Greg, St Patrocks and Oakhill in Div 1. Chevalier, St Andrews, All Saints, Central Coast Grammar, Redfields and Redlands.
Private schools that play League;
Metro Catholic Schools ( 13 schools), St Gregs, St Pats Blacktown, St Pats Fairfield, All Saints Liverpool, St Dominics, John Paul 2, Terra Sancta Schofiled, Marist Eastwood, Marist Parramatta, Trinity College Auburn, St Pauls, ST Pats Dundas, Macauly Emu Plain.
Metro Catholic Colleges ( 8 schools) De la Salle Ashfield, La Salle Catholic College Bankstown, Marist Kogarah, Marost North Sydney, Christian Brothers Lewisham, Champagnat College )agewood, Marcellin Randwick and Holy Cross Ryde.
Macarthur Independent Sports Assoc. ( 6 schools that I know of from my time at school) Broughton, William Carey, Mount Carmel, Wollindilly Anglican, Magdelene and Freeman.
That's the three I'm most familiar with and that's 27 schools. There's also a bunch that play in their own comp down in Wollongong.