Their real absolute moral values I think you mean. I think there moral theory is correct in that it is moral reality. That like everyone else, they have an iffy moral praxis reflecting ,like everyone else, an aptitude for moral confusion , I believe the conviction they have ultimately comes from God. You would have to find out from them where they think it comes from. Sam Harris could be your man for that.
In my experience, Vlad, few non-theists subscribe to objective morality and that it is more the case that it is theists, such as Alien (late of this parish) who go down the objective morality route (since they think their 'God' is the source of morals).
Your stance is confusing - you seems to be dicing and slicing terms and concepts for the hell of it.