I haven't read the paper, nor am I an expert, but the assumption (i) sounds fishy "the decision of which measurement is performed on a quantum system can be made independently of the system". By fishy, I mean obviously false. Which means being incompatible with this assumption is OK. I'm probably missing something...
"Independently" is also a loaded word - one could mean that there's no direct causal connection between the state of the system and the state of the measurement apparatus, or one could mean that those two states are (in ensemble experiments) independent in the statistical sense.
In order for Bell's theorem (and a lot of subsequent quantum theory) to work, we have to interpret causal and statistical independence as being one and the same. But the more one learns about the theoretical justification for this conflation, the shakier it seems. Bell, in particular, justified it by claiming that it was unscientific to assume that experimenters didn't have free will. Okay, sure.
Any universe where the assumption that experimental measurement settings are always already statistically correlated with the state of the system being measured (even if that correlation would have to have been established millennia ago) is fundamentally weird in certain ways - these kinds of theories are sometimes called 'conspiracy theories' as it sort of seems like all the information is there and nature is conspiring to hide it from us. But there's a whole branch of super-determinist interpretations of quantum mechanics motivated by the sense that this kind of weirdness is not as bad as the kind of weirdness we'd have to otherwise accept. This kind of work has been out of fashion for a while, but it seems to be gaining a certain amount of momentum in the last decade or so.
"Bell, in particular, justified it by claiming that it was unscientific to assume that experimenters didn't have free will. Okay, sure." You make some good points. I am not sure how Bell meant this, but read out of context, this is obviously false. Deterministic modelling (and therefore lack of absolute free will of the components of the system) is a long tradition of science.
For various reasons, in quantum mechanics, one typically excludes the observer from the system being modeled. This is obviously problematic, especially if you're doing large scale cosmology. But that's the measurement problem for you.
Regarding the context, the quote I'm thinking of comes from one of the essays in Speakable and Unspeakable in Quantum Mechanics, which is an enlightening read, both in terms of content and for its historical value. The issue, I think, is that the kind of 'conspiracy' implied by superdeterminist theories, wherein nature sort of guides our hand in picking certain experimental settings so as to hide information seems troubling to many scientists. See Zeilinger's quote at https://en.wikipedia.org/wiki/Superdeterminism
What don't you like about that? Physicists go to great lengths to make sure that random decisions are not accidentally influenced in unexpected ways, for example by basing the decision on light from quasars at the other end of the universe [1].
Some physicists argue that there might not be such thing as independence even with "quasars which are located diametrically opposite to one
another"[1].
The influence may be negligible, but it's theoretically there. The decision-maker is part of the same system (decision is happening within a system of neurons augmented with electronic tools, all of which exist in the same physical reality).
There are no neurons involved, essentially random number generators are making the decisions and in such experiments usually in the nanosecond range while particles are in flight between source and detector to ensure that the decision can not influence the creation and preparation process. And by using a source of randomness billions of light years away it becomes very unlikely that the particle source and the source of randomness could have interacted in an interesting way because the universe is to young to allow interactions due to the finite speed of light. There is of course still a possibility that an interaction happened when the universe was still young and tiny but you can probably imagine what kind of conspiracy the universe would have to have going on for that to work.
