I'm not sure where all this sort of stuff comes from but...
First of all, California does NOT have any unusual "budget issues"...
When Jerry Brown took office in 2011, he inherited a $27 billion deficit from Schwarzenegger...and proceeded to better than balance the budget EVERY year of his two terms. The state now hold a budget SURPLUS of $14.5 BILLION.
Of course, all of that is pretty much immaterial. First of all, despite being a "public university", UCLA currently gets only a small percentage of its funding from the state...and the amount has been dwindling over the years...so much so, that there has even been talk of "taking the university private". But that argument is even more immaterial than that--those figures are really only for the academic side of things. The athletic department functions and is budgeted on its own--Donors, ticket sales, television revenues and a very large contract with Under Armor--pretty much the same as most other college sports programs are funded. And the state government actually, despite some people's ill-informed suppositions, has no veto power over which coaches the University hires. Can you imagine how things might go if you allowed the state government bureaucrats (many of whom are, perhaps, alums of USC, Stanford or Cal) to be able to gum up the works?