By "independent" I don't mean "functions separately". Of course the CEO sits on the board. Sometimes the CFO is on the board too, although subordinate executives usually _should not be_ (they may _attend_ the board, but that's a different thing).
But fundamentally, the CEO _reports to_ the board. That's the relationship. And in a 501(c)3 specifically, the board have a clear requirement to ensure the company is running in alignment with its stated charter.
Whether or not this board got that task right, I don't know, it doesn't seem likely (at least, in hindsight). But this type of board specifically is there for oversight of the CEO, that's precisely their role.
But fundamentally, the CEO _reports to_ the board. That's the relationship. And in a 501(c)3 specifically, the board have a clear requirement to ensure the company is running in alignment with its stated charter.
Whether or not this board got that task right, I don't know, it doesn't seem likely (at least, in hindsight). But this type of board specifically is there for oversight of the CEO, that's precisely their role.