Ugh! In order to behave well, theists need to believe they will be punished? This again relates to our initial point of discussion, that some people primed for religion are those that need guidance -- and the threat of violence -- in order to act altruistically.
The study authors comments on the matter.
Even though the trend found in the new study was significant, Shariff cautioned, the results are preliminary. Specifically, the research focused on academic cheating, which is only one type of moral behavior. It is unclear whether the pattern of results will generalize to encouraging positive behaviors, such as generosity. Researchers should examine other impacts of how views of God may influence other types of both negative and positive moral behaviors.
In a way the findings make a certain amount of sense. If a a moral code is the functional equivalent of (Do not do bad things but if you do... "come here for your big group hug"...its is all good no worries) it may lack some function as an adequate deterrent against immoral and unhealthy behavior. The SCIENCE paper above is a good one and presents both the strengths and the limitations in the data. You cited one example of these limitations above but there are others also you will find later on. The totality of the review, however, supports my thesis.
From large village settlements at the dawn of agriculture to modern metropolises today, human beings are capable of living in extraordinarily large cooperative groups. However, extrapolating from cross-species comparisons of neocortex size, it has been estimated that human group sizes cannot exceed 150 individuals before groups divide or collapse (37). Although this specific number has been disputed (38), and whereas some Pleistocene foragers possibly lived in large villages, it is apparent that the size of human settlements since the end of the Pleistocene far exceed the limitations that kin-based and reciprocity-based altruism place on group size.
Cultural evolution, driven by between-group competition for resources and habitats, has favored large groups. However, large groups, which until recently lacked institutionalized social monitoring mechanisms, are vulnerable to collapse because of high rates of freeloading (13). If unwavering and pervasive belief in moralizing gods buffered against such freeloading, then belief in such gods should be more likely in larger human groups where the threat of freeloading is most acute.
From your comments it appears you continue to believe that our 'built-in' primitive kin-based and reciprocity-based altruism which is likely genetic is somehow an ideal. This runs counter to the vast majority of scientific thought as noted in the quote above. If you want to make this case you need to present a stronger argument then "There is plenty (of unspecified) reasons to think that it is functional" or the entirely unsupported "only religions people need moral guidance".