I deliberately left this point ambiguous. ;) The pressure on foundations to accommodate the wishes of major donors is immense and unceasing. Different foundations respond to that pressure in different ways.
I don't think it makes sense to assume that just because a project is at a foundation that it is independent by any useful definition. It's possible for dominant players to set things up such that they maintain effective control over the governance of a project which resides at a foundation. It's possible to generalize when you know the foundation, but it's not possible to generalize across all foundations.
I don't disagree with any of that. Certainly there are vast differences between Apache, OpenStack, and SPI, for example. And there can be considerable differences even between projects within a single foundation to the degree that a foundation like CNCF allows considerable latitude in how individual projects choose to organize.
In any case, if most of a project's committers are with a single company, that company is going to have a lot of control even if the project is nominally under generally neutral governance.
I don't think it makes sense to assume that just because a project is at a foundation that it is independent by any useful definition. It's possible for dominant players to set things up such that they maintain effective control over the governance of a project which resides at a foundation. It's possible to generalize when you know the foundation, but it's not possible to generalize across all foundations.