The study in question implicitly controls for a number of the factors you raise in the items it compares and convincingly demonstrates a link between contextually-defined violent action and voter outcomes. This assumes you think voter outcomes matter at all - I do, you may not.

If the events in question are polarizing and produce the outcome observed, that would be consistent with both the data and the hypothesis.

What more would you like to see? What would be enough for you? Can there be enough for you, or do you think this question is forever unknowable and to be relegated to the realm of radical hypothesizing forever?