Some assert that non-theistic morality fails to be "objective". Leaving aside for the moment why we should want or need an "objective" morality, it's worth noting that theistic morality completely fails to deliver objectivity.
The word "objective" is — like most words in any natural language — ambiguous. It has three different meanings pertinent to this context: (1) pertaining to the world outside mind or minds (as opposed to subjective) (2) consistently determinable and (3) unchanging. Conflation occurs because the truth of ideas about the world outside our minds is consistently determinable (consistent determination is necessary, but not sufficient, to establish objective truth), and many truths about ideas outside our minds are (or seem) universal, i.e. unchanging.
Any moral system established by a personal God is necessarily subjective (in opposition to the first sense of "objective"): It pertains to a property of a mind, God's mind, which is by definition a subjective entity.
Furthermore, it's logically possible that knowledge about God's mind could in theory be consistently determinable, but in practice people's statements about God's mind are strongly inconsistent.
The claim that some scripture provides a consistently determinable morality is a different claim than that God provides a consistently determinable morality. A scriptural claim, though, is no stronger than the related claim that a body of law, such as United States federal law, or the laws of the state of California provide a consistently determinable morality.
Again, while a scriptural basis is in theory an easier case to make, we find that it's does not happen in practice that morality can be consistently determined on the basis of most scriptures, the Christian Bible in particular. The sheer number of Christian sects — Catholics to Quakers — with an incredible diversity of moral beliefs testifies to this conclusion.
In sort, Jim Holman's criticism founders on the simple basis that theistic moral theories do not supply what he finds lacking in non-theistic morality.
The idea of God gives us only a theoretical ontological basis for morality.
If it were the case that we saw a consistently determinable, universal, unchanging moral beliefs; if it were the case that we saw that moral beliefs were shared across time and space in ways that could not be explained by biological similarities and social construction; if it were the case that some consistency in the world stood in need of an explanation for which local physical causality could not stand; if all these factors were the case, then God and/or scripture might serve as an explanation worthy of study.
However, the preconditions do not obtain. Theistic morality is not only an explanation in search of something to be explained, its simplest form actually contradicts our experience. We can add all sorts of ad hoc and rococo epicycles to a theistic theory of morality, but then we really do have to conclude that God is either a comedian with a very sadistic sense of humor, or just a complete bastard.