[HowlinglyMind-BendingAbsurdity]

It's not a question of being "run by the diocese." It has to do with the transfer of church property to a non-Catholic secular entity and whether that has followed proper canonical laws for the alienation of church property. As in:

"The university also claims that the sale is not subject to canon law, which requires Vatican approval for the sale of any Catholic property valued at over $3 million." http://www.catholic.net/rcc/Periodicals/OSV/98nov9.html

[It's me]

But it is my understanding that these Catholic colleges are not run by the Church and therefore not owned by the Church.

Now I am very confused. What am I missing?