Actually, the best way of thinking of the redshift is that it tells by what factor the universe expanded between the light being emitted and us detecting it.I was under the impression that red shift indicated speed they are moving away from us.
No, it doesn't. Distance is not determined from redshift; it is determined by a separate set of observations, and there is a lot of work that goes into making the determination. See Ned Wright's page on this here:The more distant they are, the faster they are receding, so it amounts to the same thing.
Don't overstate. Our current hot big bang model is well-supported, yes, but evidence is hardly ever "irrefutable" in science; there is always some chance that our best current models could be wrong.This is as far as I know based on irreffutable evidence rather than a theory.