Yes, but is'nt it also in this statement that there is some good amount of fog?
I think all agree that simply changing lables makes no differece (coordinate system).
But I think we should distinguish between choosing coordinate system, with choosing the observer. If the coordinate system can be thought as one-2-one with an inside observer view, then this are less trivial.
Some people seemt to be happy to also think that choosing a particular observer is physically irrelevant; and instead only relations between observers is physical. But this does not make sense to me; because a measurement theory cannot be sensibly formulated without this choice.
The question we should ask to clarify is this: Is the choice of observer physically irrelevant or not? Let's first note: WHOSE choice is this?
Usually we think of it as a gedanken choice made by the theorist... and the theorist is external to the system and thus this choice IS irrelevant, but....
...how does this choice look like, if we consider it beeing made by an inside observer?