Aloha Robtmc,
You are absolutely correct.
However, even nations who practice capitalism, albeit crony capitalism, also are prone to restricting gun ownership. The Philippines under the US backed Marcos regime did not allow gun ownership to its citizens. Consequently, I will add to your point by saying any nation that has a big government, even a nation that practices capitalism, does not necessarily translate to citizens having the right to bear arms.
By-the-way, I am not a leftist, but a political and economic ideological pragmatist. 
Kuleana
I was gonna let this be but something triggered in my memory about Marcos.
Marcos became a dictator after he declared martial law. He went to the owners of the various industries and demanded that if they turn over majority ownership of their businesses to him, they could continue to operate unhindered and would have the support of the government. Those that refused to give what they had worked for, had him as an enemy and were ruined or driven out of the country.
The Philippines went through a dictatorship where all practical powers were seized in the hands of a few people. This is not a democracy anymore... this is basically despotism.
When unrestrained power is placed in the hands of a few people, then that is when you run into problems whether a capitalistic or socialistic society. A true democracy has the issue of being a rule by the mob. On the other hand, a very weak government that does not have enough powers could lead to its demise until a despot successfully takes power (think Tokugawa period).
While the US government is not perfect, the founding fathers knew enough about human nature to separate out the powers of the government into three branches that are supposed to check and balance each other. When the checks and balance no longer works, then it is where we find more corruption.