Petzold does a really good job of debunking the original claim that the US is not statistically significant when it comes to the number of mass shootings. However, all of the effort he goes through only points to one conclusion: the number of shootings we have in the US isn't statistically random. All this means is that there's something causing the rate of shootings to be higher here than is expected by random influences. It doesn't point to what that cause is.
It's odd to see how statistics are abused by interest groups/media. Intuition is usually a pretty good yardstick for the validity of a statistic, insofar as knowing what kinds of conclusions should be able to be drawn from what kinds of data. If you've got a bunch of data about who likes what flavor of ice cream, it's not likely that data says anything about /why/ each person likes what they like. In the same way, it doesn't matter if you say that the US is normal when it comes to number of shootings or to say that it's abnormal as Petzold does, when you try to say /why/ this is the case, you better be drawing direct conclusions from your data.