If you believe in the Everett Interpretation, then he is wrong. The Everett Interpretation, aka Many Worlds, holds that both observer and observed are quantum mechanical systems. From this it follows that the act of observation does not produce a "collapse", but it does separate the observer into multiple observers that can't interact with each other again. So Schrödinger's cat is in a superposition of alive and dead…
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.