Does "Scientifically Random" Entail "Not Guided by God"?

It is widely held that a process that is scientifically deemed a randomness-involving process, cannot be a process that can be used by God to attain His purposes. Proponents of this view include Daniel Dennett, Richard Dawkins, as well as numerous lesser known self-styled atheists. In this I distinguish various different notions of ‘randomness’ (or ‘chance’), some of which have their home in scientific theorizing (for example in evolutionary biology, and in quantum mechanics). I next argue that none of these notions is such that if something is random in any of these senses, this entails that that thing is not created, orchestrated or sustained by God.