> In most situations, a non-profit entity cannot be owned by a corporation in such a way that would give it controlling interest.

I think you mean to say, "a non-profit entity cannot be owned by a for-profit entity in such a way that would give it controlling interest"

A corporation can be non-profit (aka not-for-profit), and there is no problem with non-profit corporation A owning non-profit corporation B. Non-profit vs for-profit is orthogonal to corporate vs other (e.g. trust) legal structure.