Yet non-profit colleges have a repayment rate of 95.3% while for-profit colleges sink to 83.3%. So it's not the 'only real difference'. But I'll give you that non-profits are not entirely blame free.
The better colleges are non-profit, which makes the non-profit group look better than the for-profit one. The higher quality students only go to non-profit colleges, and thereby lower the default rate of non-profits.
If a Devry student would not be accepted by Princeton (but would be accepted by Bumfuck U), it's unfair to compare Devry to the average of Princeton and Bumfuck. One should simply compare default rates of Devry and Bumfuck.