First, I don't see any statistics. Is that an omission or is it a bias?

Neither nor. If you have two groups where one group can do more or has the incentive to do more, then there will be done more in this group. Good or bad. My hypothesis is that the group of religious people have one incentive more to cheat, which atheists don't have: To defend their believe. This has nothing to do with statistics? If you don't like the term 'statistic' in this context, what about 'theory of probability'?

Also your comment seems to have gone from believing research results from these groups to just a general "what religious people say."

Perhaps, but does it matter? I could also claim that the question was too imprecise. What kind of research? I doubt religious people have any reason to manipulate the latest semi-conductor research results, or lie about the environmental effects of fracking any more than atheists. So, maybe I was in error to interpret it as 'research results, which in any way affect their believe system'. IMHO any other question does not really make sense.

That technically isn't what was asked, and the result is over generalized.

Technically not, true. But over generalized? Perhaps generalized, but certainly not over generalized.