I can think of three main suspicions to keep in mind when evaluating the credibility of a meta-analysis:
1. Are the studies it analyzes picked with a bias? For example, if you're looking for meta-analyses of the effects of gun control on crime, and one was published by the National Rifle Association and the other came from the Coalition to Stop Gun Violence, then you might as well just throw up your hands and go home, because each will probably have suspiciously convenient criteria for what constitutes a reasonable study worthy of inclusion in their meta-analysis.
2. Do the studies themselves suffer from publication bias? A meta-analysis purporting to show a positive effect should arouse some suspicion, because negative results often simply don't get published, and can not be included in the meta-analysis due to their nonexistence.
3. Are the methods of analysis reasonable? There are a horrifying number of ways to pull positive results out of random noise through poor application of statistics.
In this particular case, the authors don't seem to have an axe to grind, their result is negative, and their analysis is very straightforward.