> If you believe in the Everett Interpretation, then he is wrong.

If.

> And it is what quantum mechanics predicts.

It is an interpretation of what the equations predict. It is very much not the only possible interpretation, so it is not "what quantum mechanics predicts".

> But believers in other interpretations of quantum mechanics will disagree that this experiment tests anything at all.

Within other interpretations of quantum mechanics, this does test nothing at all.