You are confusing two things there - fame and inherent distinctiveness.
Marks which are "inherently distinctive" are made-up words which have no meaning other than as a trademark. Microsoft, Xerox, etc.
Coca-Cola is not "inherently distinctive". Coca-cola has a definite meaning, because it was named after its two primary ingredients in the original formulation (after carbonated water, phosphoric acid and sugar) - coca extract and cola extract. Coca and cola are both generic terms for two plants. In fact, Coca-cola is still produced using a processed coca leaf extract.
It's a good example of a descriptive term which acquired distinctiveness over time, by becoming associated with a particular product. It was so successful, that it has since become "famous" which is a term of art in trademark law referring to marks for which concurrent uses of the mark by others would reasonably be believed by consumers to have originated with the primary mark owner.
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Interesting, I did not know that background on Coca-Cola, I was just using an example that popped into my head. So basically my 'theory' is right, I just used a bad example?