Everything becomes blurry when institutions accept public funding (for research, etc.) as well as accepting tax breaks or exemption status.

I'm of the opinion that we actually require far too little of organizations that accept public money. We should be getting more public-good guarantees to go along with that money. (I'm thinking stuff like: any research done with public funding should have free-to-access results, published under a permissive copyleft-like license.)