I just want to highlight most essential parts in question:
the choice of the interferometer configuration, the applied voltage on the EOM is randomly
chosen in real time, using a Quantum Random Number Generator (QRNG) located at the output
of the interferometer.[...]
by sampling the amplified shot noise of a
white-light beam. Shot noise is an intrinsic
quantum random process, and its value at a
given time cannot be predicted (23). [...]
performed with the EOM randomly switched
for each photon sent into the interferometer,
corresponding to a random choice between the
open and closed configurations. [...]
raw data were saved in real time and were processed
only after a run was completed. [...]
We even can change experiment in the way that all equipment would be powered-on/off by some random process, with experimenters miles and miles away and not aware of when experiment would start. Recorded results would give the same effect.
So... Are proponents of quantum mysticism wrong? Apparently, big YES.