I decided to actually look for the journal paper to which the article refers. Was pretty easy to find, leading me first to wonder why they didn't provide a direct link to it, given that it's published in an open journal (PLoS ONE).
http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0017006
From a group of 268 people, just 19 identified as "No Religion", and another 17 identified as "Other Religion". The remainder were 113 non-born-again Protestants, 97 born-again Protestants, and 22 Catholics. The sample was "largely Southeastern Protestant Christians", yet they somehow claim meaningful results from such a sample.
In other words, nowhere near enough for any sort of accurate observation, except perhaps for born-again vs non-born-again Protestants. Seemingly notable is that they appear to have taken "non-born-again Protestants" as their "control"... which really does seem rather skewed in-and-of itself.
And, if I understand the statistical notation (and I'm the first to admit that I'm no expert in statistics), the only results (in terms of religion itself) that are even close to being significant are the "born-again (baseline)" and "Life-changing Religious Experience (baseline)" - these two represent categories where, at the initial interview, they reported either being born-again (self-identification), or fitting the born-again description but not identifying with it.
On the other hand, "Private practice" seems to be positively correlated reasonably with size of hippocampus. So does "Social support" (positive correlation), "Stress" (positive correlation, curiously), and "Age" (negative correlation).
If you, alternatively, accept that born-agains, catholics, and those with no religion are indicated as having more atrophy, then you must also accept the other result that goes with these ones: that those who follow an "Other Religion" actually have less atrophy. And yet, the paper didn't even mention it, other than including the "Other" row in the table.
In short, this seems like a case of trying to make a lot more out of a study than really was the case. It looks to me like they didn't get any truly meaningful results. And yet, they proclaim a "large sample size", despite getting less than 20 people of "no religion"... yeah.