Yes, but private foundations are only paying for the incremental cost of their funding, not the base cost. If you are flying a plane from LA to Chicago, the incremental cost of flying that plane on to Detroit is pretty low; a low overhead on the direct costs of that additional leg makes some sense. The private foundations are like the additional leg, they aren't paying for the fixed costs of running the airline.
When looking at the whole system it clearly becomes woefully inadeqate. To extend the example, the only direct costs of an airplane flight are the crew, the fuel/food, and any airport fees. Could you run the rest of an airline (training, ground staff, scheduling, booking, IT, maintenance) on 15% of the crew+fuel costs? Not even close.
If you look at federal contractors and other companies, the overhead on staff is probably closer to 100-200%, so 50-60% is very defensible.
When looking at the whole system it clearly becomes woefully inadeqate. To extend the example, the only direct costs of an airplane flight are the crew, the fuel/food, and any airport fees. Could you run the rest of an airline (training, ground staff, scheduling, booking, IT, maintenance) on 15% of the crew+fuel costs? Not even close.
If you look at federal contractors and other companies, the overhead on staff is probably closer to 100-200%, so 50-60% is very defensible.