Poking around the linked site, I find the organization, the National Healthy Marriage Resource Center (which was created two years ago with funding from the Bush Administration through the DHHS, right around the time the Gay Marraige issue first reared its head), lists several people associated with the arch-conservative Heritage Foundation on its Advisory Board. The site also lists various hubs of activity including its research hub at Brigham Young University, and its faith-based hub at Norfolk State University in Virginia. As the son of an ex-Mormon, I can tell you that BYU is very unlikly to promote any research that suggests that religious people may be immoral to an equal or greater degree than heathens.
However, they do cite their source for that statistic: Atkins, D.C., Jacobson, N.S. & Baucom, D.H. (2001). Understanding infidelity: Correlates in a national random sample. Journal of Family Psychology, 15, 735-749, which some citations list as Atkins, D.C., Jacobson, N.S. & Baucom, D.H. (2001). Understanding infidelity: Correlates in a national random sample. Journal of Family Psychology, 15(4), 735-749. Unfortunately, I can not find a free online version of this article.
What I DID find was the farewell letter(pdf), two years later, of then-editor of the Journal of Family Psychology (a peer-reviewed publication of the APA), Ross D. Locke, in which he lists as among his proud accomplishments the publication of various special issues and sections, including a section on “Families and Religion”, in issue 15(4), suggesting the possibility that the article was specifically solicited for that sepcial section.
The authors of the paper itself are:
[li]David C. Atkins, currently an Assistant Professor of Psychology at Fuller Theological Seminary[/li][li]Donald H. Baucom who studies and advises couples who are supporting each other during cancer treatment, but who was listed last year as a “forgiveness researcher” by A Campaign for Forgiveness Reasearch.[/li][li]Neil S. Jacobson, who seems to be a straightforward and highly respected psychology researcher. Of course, if in the very final preparation of the article for a special issue of families and religion in 2001, some undue relisious bias had crept in, he would have had little to say about it, as he had been dead for two years.[/li][/ul]
So, while the article itself is not easily available to us to review its methodologies or conclusions (or their correct description by the NHMRC), I’d have to say there is a higher-than-background-noise possibility of a pro-religion bias in circumstances surrounding the presentation of that statistic.