From what I read in the article and in the Development Code, it's not that you have to get approval to paint a facade beforehand, it's just that it has to fall within the Unified Development Code for Starkville, which says "The primary facade colors shall be low reflectance, subtle, neutral, or earth tones. The use of high intensity, metallic flake, or fluorescent colors is prohibited.", but doesn't provide a palette of what's included in that. The owner even said, it's not clear what's included and the board couldn't provide a palette. If you Google 'earth tones', you'll see greens and yellows and they don't look far off from the street view in the Google Maps link dorndawg posted. I feel like 'subtle' and 'neutral' are pretty subjective.
starkville.municipalcodeonline.com
I think the funniest thing is that they're letting him keep the bright purple awning, which is objectively the most garish color in the whole facade.