“Hubble mistakenly claims the cosmological redshift proves all galaxies are receding from us”.
He may have thought that in 1929 but, as you may well be aware, he later changed his mind. I wrote about this in an article some time ago:
Here is the relevant passage:
“...in 1935, somewhat alarmed by the velocities involved, Edwin Hubble himself suggested that some mechanism other than expansion might be responsible for producing the cosmological redshifts. And a year later, armed with a much better set of data, Hubble wrote a follow-up paper that came out decidedly in favour of the tired-light model. His data agreed with a stationary Euclidean universe in which the redshifts were due to some unknown effect, which caused photons to lose energy as they travelled through space. He was therefore agreeing with Nernst, Zwicky, and Regener”
refs:
E. Hubble and R. C. Tolman, “Two methods of investigating the nature of the nebular red-shift”, Astrophysical Journal 82 (1935): 302–37
“Effects of red shifts on the distribution of nebulae”, Astrophysical Journal 84 (1936): 517