Empirical Support for the Natural Law?

Penn law prof Paul Robinson, Penn psychology prof Robert Kurzban, and Vanderbilt law/biology prof Owen Jones have posted their paper, The Origins of Shared Intuitions of Justice.  Here is an excerpt from the abstract:

Contrary to the common wisdom among criminal law scholars, the empirical evidence reveals that people's intuitions of justice are often specific, nuanced, and widely shared. Indeed, with regard to the core harms and evils to which criminal law addresses itself - physical aggression, takings without consent, and deception in transactions - the shared intuitions are stunningly consistent, across cultures as well as demographics. It is puzzling that judgments of moral blameworthiness, which seem so complex and subjective, reflect such a remarkable consensus. What could explain this striking result?

The authors theorize that one explanation may be an evolved predisposition toward these shared intuitions of justice, arising from the advantages that they provided, including stability, predictability, and the facilitation of beneficial exchange - the cornerstones to cooperative action and its accompanying survival benefits. Recent studies in animal behavior and brain science are consistent with this hypothesis, suggesting that moral judgment-making not only has biological underpinnings, but also reflects the effects of evolutionary processes on the distinctly human mind. Similarly, the child development literature reveals predictable stages in the development of moral judgment within each individual, from infant through adult, that are universal across all demographics and cultures.

Or do the shared intuitions suggest a common author?  Is this evidence of the law written on our hearts?