Au Contraire. From the bylaws posted publicly so far, it seems, they aren't truly independent of each other.

Microsoft is the "Founding Member" of the .NET Foundation. They are entitled to appoint an Exec. Director (ED) and the board has no say in this matter (The current ED is the person who forced a commit on a member project). The ED's tenure has no expiry other than when Microsoft feels the need to change (or they leave). All other board members are elected for a set term.

Lastly, the ED can block any board resolution; aka, the elected board needs Microsoft's blessing to do literally anything.

Source: https://github.com/dotnet-foundation/Home/discussions/39#dis...