If you do not like the Red ball thing, feel free to invent another test, such as flipping a few bits on another computer.

No, it's the same. Specifying what a physical "computer" is is hard.

No as that would lead to an decrease in mutual information between the two models.

What is a "model"? How does one construct a model of the universe? How detailed must it be, whatever it is? What resources should be expended on making a more accurate model? Given two "models", how accurate must a calculation of mutual information be? What if it can't be accurate? What is the tradeoff between making it more accurate and not rewriting the universe with machinery for making it more accurate? Etc.