The fundamental problem with non-profit executive pay is that they earn their keep. Even more directly than CEOs in a for-profit space. The CEO of a non-profit has approximately one job: convince rich people to give the non-profit large amounts of money. It turns out, rich people know other rich people. And rich people who know how to convince other rich people to give them large amounts of money are a scarce resource, that non-profits squabble over.
So you've got a scarce labor pool, with expensive lifestyles, and a very directly obvious ROI. That alone is a recipe for high salaries. Combine that with the inflation that comes from the fact that for-profit executives get to hide a huge portion of their compensation as stock, whereas non-profits pretty much exclusively offer salary, and you end up with apparently bloated non-profit executive salaries.