There are many toxins, poisons, allergens and irritants found in nature, natural is not necessarily better. Our hair evolved to be cleansed by water and conditioned by sebum, it didn't evolve to have plant extracts applied to it any more than it evolved for laboratory made ingredients.
Many ingredients in haircare products are backed by research, they do patch repair damage, strengthen the hair, increase elasticity, impart shine. Some of these proven ingredients are natural and some are manmade.
That website you linked to is a sales site, it's likely to be heavily biased. Check out the 'curl chemist' articles by Tonya McKay here on NC, the Natural Haven, Swiftcraftymonkey blog, Barefacedtruth, the free papers on the Journal of Cosmetic Science site.
I use Weleda baby calendula face cream, my sensitive eczematous skin loves the skin similar lipids in lanolin. I've also used the baby shampoo and body wash and it was pretty harsh on my hair and the body lotion which I found greasy.
Any 'true' conditioner is based on the major emollients (fatty alcohols and cationic surfactants), emollients provide softness and 'slip', and can also gently cleanse. Most of these are derived from cheap natural oils like palm fruit or coconut. These same emollients are found in many natural or organic products, including CURLS and Weleda.
Ingredients Commonly Found in Hair Care Products