Only the things that are directly observed/measured should be talked about as facts, like the redshifts in the spectra of distant galaxies. If you say these galaxies are flying away from us, you are making an inference, so that is not a fact. The radial velocities of galaxies are inferred, not directly measured.
Anything that the Big Bang explains, like the CMB can be explained in other ways too, i.e it is simply the blackbody radiation emitted by matter in interstellar space which reaches a minimum temperature under starlight. It was worked out that this would be 3K before the CMBs discovery, whereas the Big Bang Theory predicted a 50K temperature beforehand.