Let's weaken it slightly. Consider Schrödinger's cat. Let's assume the Copenhagen interpretation, and assume that collapse does not happen until the box is opened.

Now let's modify the experiment to assume a hyper-intelligent cat, with access to a full physics laboratory inside of the box.

QM predicts that there is no experiment that is possible for the cat to conduct that can tell whether collapse happened. The QM description of what's going on in the box is guaranteed to be alien to the cat's experience, but perfectly predicts what the cat does experience. Furthermore, even though in this hypothetical, collapse happens when the box is opened, there is no experiment that can be done by the outside experimenter which can verify that collapse happened when the box opened, and not before. Nor is there any experiment that the experimenter can perform that confirms that collapse does not happen afterwards.

And yes, this includes attempts by the cat to confirm the Born rule. As far as the cat can determine, the Born rule will be true.

Therefore our assumption in this hypothetical that QM describes the cat leads to MW being true for the cat no matter what is ultimately true.

And this is what I mean by saying that, to the extent that the experimenter is described by QM, MW is true.