Aside: (Personally, I see this more as Bohr's way of dodging questions he had no answer to, and not a viable way to think about Quantum Mechanics. A better answer would have been "I don't know. Let's figure it out." But that was impossible for political reasons. Bohr was being attacked by Einstein for 's sake. He can be forgiven for adopting Ali's "rope-a-dope" tactics if he felt that Einstein was trying to destroy his entire field in its infancy. But I find "there is no quantum world" simply unacceptable.)
Now to answer your question as best I can, an interaction must collapse the wave function when it is required to fulfill a conservation rule. For example, if an electron is captured by a nucleus it becomes bound and emits a photon. This is an interaction that must conserve momentum, angular momentum, energy, and charge. Because of that, the electron can no longer be represented by a non-localized wave function. The universe must concentrate those properties down to a point in order to "do the accounting" necessary for the conservation rules.
No, I don't know how it does that. But then, NONE of the available interpretations answer that question. This indicates to me we are thinking about it wrong.
What I like about Stuckey's paper is that it adds another factor: besides conservation rules the universe seems to require that "measurements" obey the Relativity Principle (No Preferred Frame of Reference). I have yet to figure out how to incorporate that.
