You have to be actively in the small circle of people who are working this issue to spot problems with the way the data is analyzed.
There can be problems of definition which make the analysis silly, even if it is mathematically valid. These problems can easily come from false premises about reality, which are nearly impossible for those that hold them to spot.
One “tell” that I would like to have the authors explain, is the choice of the year 2000 at the start of their study period. They repeatedly state that Florida was the first state to pass such a law, in 2005.
Why then did they choose the year 2000 for the start of their study period?
In many studies where the numbers give data that is ambiguous, an author can bias the results to get what he wants by choosing the time period under study.
Here is an article that details some of the problems with the FBI definition of justifiable homicides:
http://www.freerepublic.com/focus/f-news/2894470/posts