American culture and laws came from the English, French, and Greco Roman legal systems, as did our religion from Christianity not the pagan religions of native Americans. Democracy comes from the Greek, demos scratein. Our written constitution also did not come from native America. The Indians didn't even write or have books other than for symbols on natural material like stones. He didn't misspeak. He spoke what's true but is just trying to protect his high-paying job like most people who don't have the guts to standby their beliefs anymore. Rather than being fired, if CNN had any guts themselves, they should have debated his points. They're starting to look like LuLa. 
I think Republicans always start from a losing position on cultural talks such as this. As far as I am concerned, culture breaks down into two different parts, the superficial and the significant.
The superficial aspects of culture are the food you eat, art, your dress, how you talk, what you read, etc. These are all things that could provide meaning to your life, but ultimately do not effect your life in any significant way.
Then there are the significant aspects of culture, such as the way in which you are governed, your granted rights, the court system that is used, etc. These all have profound effects on your life, all of which can vary greatly even between neighbors. There is a drastic difference in Mexican courts and American courts.
As an example, there is an Italian restaurant near me owned by a Chinese immigrant; he is also the head chef. He likes Italian food more then Chinese food, so he decide to study Italian cooking and opened an Italian restaurant when he came to America. I am sure he gets great pleasure from cooking Italian food. However I would bet him opting to work in another cuisine then his own pails in comparison as to how it effected his life vs. moving from China to the USA with our Anglo-Saxon culture of rights, governance and courts.
So, of course Santorum said nothing wrong. It's just people tend to think of the superficial aspects of culture first, of which there is a great deal of Native American influence, and Santorum did not clarify he was talking about governance and rights. Now how you do this in a sound bite so people know which part of the culture you are talking about is a whole other question, something I do not think is possible.
It's like trying to state the true purpose of the 2nd amendment, which is giving the states a way to protect themselves from a tyrannical federal government through forming a militia that can only be formed effectively and efficiently by having an already armed citizenry with arms on par with regulars in an army, which is why people need the right to bare arms. Instead, saying "it's for personal protection" is just so much easier.