Theist Vs Atheist Morality

Many theists say, correctly, that morality or integrity is doing what is right when no one is watching.  However, many also say that is difficult to do what is right if one does not accept a deity watching. In my opinion, this counterfeits the argument, as "someone" IS watching.

Science-based thinkers understand that our morality or integrity comes not from a being outside of us but from evolution and socialization. These processes have given us empathy, and THAT is really why moral humans act the way they do, regardless of theological perspective. Research shows that theists do not act any more moral than atheists as groups (link). As a personal example, when I was religious I acted out of empathy and I continue to do so presently.  In other words, my feelings and my behavior in this regard have not changed.