Indeed! I haven't been able to get through a sitcom or (gasp!) ecchi anime in years, but I had never thought about the pervasive thematic similarity between the most popular American television genre and the most socially retarded (not a small accomplishment) subgenre of Japanese anime.
In fairness, lately I have been quickly overwhelmed by the awfulness of every prime-time TV show. If it's not on HBO, Showtime, or AMC, you can probably forget it; I don't mean to imply that those channels are unending fonts of quality, either, though, just that they seem to have a monopoly on it. There are certain pervasive cliches that I refer to as "network TV *" (e.g. "network TV" sex, precious grade-schooler, teenager, submissive husband, etc.), and the sitcom seems to be the ultimate distillation of such tropes. I have not yet been married, but I feel fully qualified to write an average episode of an average marriage sitcom. Network TV police drama is a close second; I couldn't presume to write an episode of "The Wire" without at least as much research and experience as David Simon--and even then, I would have get years of practice with scriptwriting--but shows like "CSI" or "The Mentalist" or "NCIS" are another matter altogether.
Although I don't have enough evidence to make a claim about the general population (indeed, if anything, I only have counter-anecdotes), I personally seem to have a regulation mechanism for media consumption. After I watch enough exemplars of any TV or movie genre (the threshold seems to vary according to maturity and innate or early-childhood-born preferences for the core content of a genre: it took hundreds of action movies to sour me, a few dozen TV dramas, and a handful of sitcoms, but two ecchi animes were more than enough when I discovered anime at age 17), the banality and derivative quality of the writing become painfully apparent, and my enjoyment is lost.
While I'm not sure about the specific genesis of my system of morality (for that matter, I can't confidently and accurately describe what it is), at least I can say that repeated exposure to unsophisticated or redundant themes makes me want to avoid further experiences with them at all costs. This is true of books and video games as well, the greater diversity of those media (especially written media) just makes it less obvious. I feel I can be on somewhat firmer ground in claiming that the average "serious gamer" tires of violence for its own sake very quickly, and requires increasing levels of sophistication and novelty in gameplay as well. 7-14 year-olds (the subjects of the study) may not be too far advanced in such tastes yet, but they surely will be. I realize that coming to demand variety in one's violence is far from a refutation of the claim that early exposure to violence impairs the development of empathy, but it at least speaks to the improbability of some positive craving or tendency to violence being created.
Perhaps the best source of empirical data on (late adolescent and adult) violence conditioning comes from the experience of the U.S. armed forces over the past century. Especially since WWI, there has been a constant reevaluation and evolution of soldier training practices, the result of which has been that increasing percentages of infantry troops actually fire their weapons, and do so with increasing purposefulness, when contact with the enemy (militarily) demands it. Nothing close to a "perfect" regimen yet exists, however, since even after very rigorous modern training, a large portion of deployed soldiers end up with traumatic mental disorders after experiencing the actuality of combat and killing (even though there is very likely much less "baseline" empathy between a contemporary American soldier and an impoverished non-English-speaking Muslim irregular than there would be with, say, an average WWII Wehrmacht private or even a VK). It is almost certainly much harder to desensitize a soldier of eighteen or more than a seven year-old, but such data do demonstrate that "real" violence has a vastly greater emotional impact than controlled training. For the 7+ age group (which can almost universally distinguish fantasy from reality, at least as far as video games go), it seems likely that actual interpersonal experiences with bullying or abuse by adults would similarly far outweigh the influence of media on mental development. If an absence of bullying and abuse proves insufficient to develop empathy, it seems unlikely that the (mere) absence of violent media would be different.
From a policy perspective, one might argue--aside from privacy, impracticality, or slippery-slope reasoning, that is--that legally restricting violent media from minors will only have the effect of arbitrarily punishing the (relatively) well-adjusted, since those who are are theoretically harmed by violent media are probably doomed by their genetics and/or upbringings alone. It is hard to imagine anyone removed from the hysteria of their arrest and trial seriously or successfully arguing, for example, that the infamous Leopold and Loeb were otherwise perfectly normal teenagers who were then unhinged by reading Nietzsche, or conversely that their actions represented anything like a standard reaction to the cultural and literary influences to which they were exposed.
Returning specifically to TFA, I will observe (regrettably, not deviating far from the /. party line) that based on the sparse summary of the pre-print article in the dubious sociology journal (publishing easily misunderstood, loosely empirical studies that promote the simplification of politically charged issues is many sociologists' raison d'être), it's hard to believe that the researchers discovered much evidence of causality one way or the other. Besides--regardless of the conclusions here--none of these sociology studies can legitimately pretend to definitiveness: even in the (marginally) more empirical field of psychology, there is little consensus about the primacy of or requisites for direct parental influence on child development. Even the finding of an overwhelming correlation in a study like this one would serve mostly to indicate future lines of inquiry, not to suggest or support an developmental model for empathy. Not much is known for sure about child development, including a good reason to believe that it is a simple or easily explicable process.