If I'm able to understand how master/publishing rights splits work it will help before moving forward.
They're the same as every other right. If you need one right, you need one right. If you need two, you need two. It might help if you stop thinking they're connected, even though they may be intertwined....
Much like driving a car. You need a license to drive the car, but you also need permission from the owner to drive the car. While they're intertwined (as in you need both), since one party can give you one of those rights, the other isn't necessarily part of that transaction. You may need to clarify and if necessary source permission from the other entity.
So to answer your original question, it'll depend on what you had quoted.