I don't think there's anything special about training in the country of origin, from an intensity standpoint, or even necessarily from a depth of understanding. In some cases, there is greater depth of understanding (higher concentration of highly experienced practitioners) and in other cases there's just more adherence to the traditional methods (which may be good or may not). And intensity can vary by culture (which may favor the country of origin or not) and by school/instructor.
I agree, mostly. I think a person is better off in the country of origin if they study American Karate.
Although I doubt it's taught anywhere else.