The rationale of not apologizing

I have lived in the US for 20 years, I still keep learning various cultural aspects of this country.  Since the country is so diverse, I have never been able to construct the image of "the typical American". It seems there are always two opposite groups on everything.

I have been wondering why some Americans vehemently oppose issuing apologies to other countries.  Senator Santorium finally gave a crystal clear explanation on NBC's Meet the Press show yesterday.  When asked about the Koran burning by the US troops that deeply hurt the feeling of Muslims, he said it is mistake, but the US should not apologize because it was not deliberate.  Following this logic, one should not apologize if he kills a person by mistake, say, in a hunting event as long as it is not deliberate.

Though his explanation is crystal clear, it is unclear to me how many Americans share this view.