I use the India product line from I.C.O.N., specifically the shampoo and conditioner. On their bottle, they indicate that it's vegan. I emailed them asking to confirm that these products were certified organic and contains no chemicals. They confirmed that this is accurate. I would greatly value your opinion.
Just because a product is vegan, doesn't make it safe, natural, or organic. Sometimes when we think of vegan cosmetics/personal care products, we imagine that it's all made up of vegetables. That somehow some kale was turned in to a puree, some essential oils added and now it's a shampoo. But when a product is labeled as "vegan" all that simply means is that there are no animal-derived ingredients. Petroleum isn't an animal by-product, so, technically it's "vegan." Petroleum-derived "fragrance" and coal-tar derived artificial colors are "vegan" too. "Vegan" doesn't mean it's all vegetable-based, just simply absent from animal-derived ingredients.
So, let's look at one of the products in question, the I.C.O.N. India shampoo. They don't list their full ingredients on their website (our first red flag here.) But I found them listed elsewhere:
Water, sodium cocoyl isethionate, sodium methyl cocoyl taurate, acrylates, crosspolymer, cetearyl alcohol, ceteareth-20, moringa oleifera seed extract, shea butter, panethenol, hydrolyzed soy protein, rice amino acids, spirulina, fragrance.
Ceteareth-20 is an ethoxylated chemical, meaning that it's created with the carcinogen ethylene oxide, traces of which can remain in the product, along with its carcinogenic by-product 1,4-dioxane.
Fragrance can be anything from a list of over 3000 different chemicals, including endocrine-disrupting phthalates, neurotoxins, petrochemicals, and allergens.
Acrylates are plastics known to be strong irritants and allergens.
Sodium cocoyl isethionate and sodium methyl cocoyl taurate are mild detergents, however, they're new chemicals to the market and not much else is known about them. While they don't have any known health effects, they are hardly organic as you state the manufacturer claims.
So, while there may be a couple of natural ingredients in the shampoo, and it may be vegan, it's hardly even natural. (See my definition of natural here.) If they have claimed that their product is organic, either they're blatantly lying or don't understand what organic really means.