I currently run a small Non-Profit theater company and I have woked for Non-Profits for most of my adult life. I think for some Non-profits, the larger you get, the further you get away from you mission and that is where things get dicey.
The organization that I run now runs on the most shoe string of budgets ( I am the Artistic director and President of the Board and receive zero pay, our actors receive a Stipend and our teachers are paid. The rest is primarily volunteer). If it wasnt for our tax exempt satus, we would be screwed. There are plenty of large Non-Profits that pay their high up staff quite a large salary, but the law says they are allowed to recieve a fair and reasonable salary based on their job description. Sometimes I think that is unfair when the low end staff is struggling to make rent because they are working in a field they love.
Sadly, I think it is true hat a lot of these large charities that are started by sports figures, celebrities and the like are meerely a way to hide funds, make more money or re-direct their earnings to not pay taxes and that sucks.