Jlgreco probably meant: "did they not add coloring [during production]", for which to make sense the color would have to be added during the production, which could very well be; the article probably meant "found a chemist who could remove the color", implying the color is a by-product of the production and comes from other ingredients. So, the article is not explicit about this, but the whole context would lead me to believe that it is the second explanation that was meant.

I suspect that if they were only making small quantities of it, they might not want to mess with their working production setup, and so it could be more economical to mass produce the coloured product and get advice from their staff food chemist on how to remove the coloured compounds for the small special order.

But why would they need a chemist to tell them how to simply not add color?

I think you're answering your own question here. Coke without coloring isn't completely clear, so they hired a chemist to mask whatever natural color coke has. At least that's the impression I got from that sentence.

I assume in the original recipe the color wasn't added, but was a consequence of how it was produced then.