Not necessarily. First we have to ask where the data comes from and how it was collected. The National Crime Victimization Survey (NCVS) is conducted by interviewers who enter randomly selected households and ask people about their experiences. This method has the advantage of counting crimes that were never reported to the police, but only if the person being interviewed is comfortable talking about them at home. A recent report of of the National Research Council discusses this problem with the NCVS in detail:
Because most rapes and sexual assaults are committed by individuals whom the victim knows, respondents may be reluctant to disclose their victimization during an interview that takes place in the home within earshot of other family members. The training for NCVS interviewers does not stress privacy, and even if adequate training were provided, the nature of the survey—a general-purpose criminal victimization survey—means that interviewers very rarely get positive responses on questions of rape and sexual assault.
The report concludes that the NCVS is "likely undercounting incidences of rape and sexual assault," and notes that other surveys consistently report higher numbers. Since we'd expect women to be more likely to talk about domestic violence if their partner isn't around, we should expect that the NCVS under-reports violence against married women specifically. This means that the difference between the married and unmarried rates of violence is at least in part an illusion, an artifact of the survey method. We just don't know how much of this difference is real.
But let's suppose that these numbers are accurate, or that the general trend of less violence against married women still holds. Wilcox and Wilson still have a second big problem: the confusion between correlation and cause.
They are careful with their language, writing "married women are noticeably safer" which is both perfectly true and completely misleading. We may read "married women are safer" but we probably understand it more like "married women are safer because they are married." Not only are our minds always looking for causes, but the rest of the article reinforces this notion. It puts an idea like this in your head:
And really, what's so unreasonable about that? A good marriage is something that should feel safe—and as the authors point out, it's not unreasonable to imagine that a good man will protect his wife from harm.
Yet all we know is that there is a correlation between marriage and a lower (reported) rate of violence against women, and any correlation goes both ways. So let's try it this way instead: "safer women are married." If that sounds weird, it's probably because you were thinking of "married women are safer" as a causal statement.
"Safer women are married" says the exact same thing as far as the data is concerned, and it's reasonable to imagine that the causality actually goes this way: women who have never been a victim of violence might be much more likely to get married and less likely to get divorced. Or there could be a third factor that influences both safety and marriage. A woman who is already in a safe situation for some other reason—perhaps she is financially secure—might be more willing and able to get married. In fact, income does seem to be part of the story: Marriage rates are lower and falling faster among lower income families.
Wilcox and Wilson know that these alternate explanations are possible. They write,
For women, part of the story is about what social scientists call a “selection effect,” namely, women in healthy, safe relationships are more likely to select into marriage, and women in unhealthy, unsafe relationships often lack the power to demand marriage or the desire to marry. Of course, women in high conflict marriages are more likely to select into divorce.
Yet the rest of the article is written like they know for sure that marriage causes safety; that's the headline. They repeat the same correlation/causation language fudge several times, writing "Women are also safer in married homes" and "What’s going on here? Why are women safer when married?" They could have written "why are women married when safer?" because it's just as true, but they didn't.