How can Valentini's subquantum measurement work if particles cannot affect the wavefunction?

In Brown and Wallace’s 2005 paper, it is argued that the corpuscles in Bohmian mechanics are ontologically unnecessary, as they play no role in solving the measurement problem. Instead, they argue, the corpuscles merely anoint by fiat a particular branch of the wavefunction as existing for real, because the corpuscles do not influence the wavefunction. Thus, there are still superimposed "empty branches" that contain no corpuscles but continue to evolve according to the Schrodinger equation; these "ghost worlds," if I’m understanding correctly, contain everything of interest: people, trees, wars, etc., just no corpuscles. For this reason, David Deutsch called it many-worlds in denial.

In Antony Valentini’s 2008 reply, he says Bohmian mechanics cannot be many-worlds in denial because if primordial matter in quantum non-equilibrium can be obtained, then we would be able to violate the uncertainty principle and measure the corpuscles (he calls this subquantum measurement). Thus, it is a fundamentally different physics.

This is where I’m confused. If we were to perform a successful measurement and gain information on the corpuscles, that would imply at the very least that the wavefunction of the observer’s brain would have been affected. Furthermore, the observer could choose to run an experiment to affect another system’s wavefunction in one way or another based on the information. So how does subquantum measurement work if Schrodinger’s equation is closed? The original paper presenting subquantum measurement is here but the math is over my head.

Related: Does Bohmian mechanics really solve the measurement problem?