The observer’s consciousness is still involved. Imagine that the Born rule isn’t a law of the universe itself, but of consciousness. The universe evaluates all branches. Consciousness follows the branches in weights following the Born rule. The conscious observer always finds themselves down a series of branches that were selected by the Born rule, and it’s easy for them to take measurements to confirm this. The Mathematica 5000 machine that’s come down this series of branches has made measurements from experiments and has found that the Born rule has held. It only comes up with this result because this is the version of the machine that has followed the observer’s consciousness through the branches. In the raw universe, most worlds have the Mathematica 5000 machine finding that Born’s rule does not hold; these aren’t the worlds that conscious observers usually find themselves in though.