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Tamara, I am trying to download your citation, but unfortuantely am traveling right now, and this computer doesn't seem to like .PDF docs, I will read it carefully when I return home, however.
I will point out that, aside from the sources, the frequency graphs on the opening page do not attempt to assign causality, they are simply showing what is occurring, rather than why it is occurring. The latter is worthy, but a more difficult goal. Certainly, they show exceptionally high rates of firearms related deaths in the US - noone else is even close. Further, these data are averaged over entire countries, they are not a small sample, and so aren't troubled by sampling variance, and don't have any sampling bias.
As to the Vermont - NY comparison, I don't say there can't be anything in it, but the trouble is, that many things are different between NY and Vermont, not just gun laws. For instance, while I lack a citation, I suspect that Vermont probably has more cows per acre than New York. My point is not to redicule. My point is just that it's dangerous when attempting to find causality between two systems that differ markedly in scores of factors, to reach in there and pick out one possible factor as the cause - the odds are actually against it being true.
To avoid false correlations, it's best to use large samples, which carefully avoid bias, and to control for confounding factors.
To avoid false claims of causality, it's best to first do the above, and then have a logical mechanism that explains the proposed causes... the data and the model used to explain them can then be scrutinized by others who face a similar burden in either supporting, modifying, or refuting - this type of inquery and dialogue are really the foundation of science.
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