I’m not sure I follow your argument, but if I understand you right, I don’t believe what you’re quoting is relevant. From the article you are (I think?) criticizing:
We measure a Bell signal S of 2.0732 ± 0.0003, exceeding the maximum value |S| = 2 for a classical system by 244 standard deviations. In the experiment, we deterministically generate the entangled state, and measure both qubits in a single-shot manner, closing the “detection loophole”[11]. Since the Bell inequality was designed to test for non-classical behavior without assuming the applicability of quantum mechanics to the system in question, this experiment provides further strong evidence that a macroscopic electrical circuit is really a quantum system [7].
https://web.physics.ucsb.edu/~martinisgroup/papers/Ansmann20...
That says in plain English that they have not assumed that this system behaves according to quantum principles. In fact, it is precisely the opposite: the quantum nature of this system is a conclusion of their results. It would be statistically impossible for any system following classical rules to produce the same data.
(It bears repeating that the math underlying that conclusion is truly not very complex, and it is very, very well studied. If you can show that it’s flawed somehow, don’t bother publishing— just post your proof here and I’ll, uh... pick up the Nobel for you.)
The only caveat is that this experiment closes the detection loophole, but not the locality loophole; it is theoretically possible that a classical signal could be sent from one qubit to the other quickly enough to fabricate this data. There’s no particular reason to suspect a secret signal is in play, but it isn’t theoretically prohibited.
Assuming you haven’t found a flaw in their mathematics, and that you aren’t alleging that the researchers deliberately fabricated their data, the locality loophole is your best (and likely only) avenue to dispute their conclusions. However, if you wish to pursue that, you should keep in mind that there are many other experiments which close the locality loophole but not the detection loophole, and, since 2015, several that close both. Three-card monte may be a better investment of your time.