Babies have high level of an enzyme called lactase in their small intestine. This allows then to digest the lactose in milk. The persistence of lactase in adults is genetically-determined and highly variable.
In cultures and geographical areas where milk drinking has a long history (Northern Europe, parts of Africa and Arabia) a high proportion of the population shows lactase persistence (Beja-Pereira et al, 2003; Hollox et al, 2001). This suggests that there has been an evolutionary shift towards lactase persistence paralleling the development of dairying approximately 8-9 thousand years ago.
Thus, whether or not you consider the drinking of cow's milk 'natural' is a matter of perspective. A person with lactase persistence is able to drink milk in reasonable moderation and experience health benefits rather than deficits.
Reference:
- Beja-Pereira, A. et al. (2003). Gene-culture coevolution between cattle milk protein genes and human lactase genes. Nature Genetics, 35, 311-313.
- Hollox, E.J. et al (2001). Lactase haplotype diversity in the old world. American Journal of Human Genetics, 68,160-172.