The Who, What, When, Where and Why of Chemistry
Chemistry is not a world unto itself. It is woven firmly into the fabric of the rest of the world, and various fields, from literature to archeology, thread their way through the chemist's text.
The news report offers a number of theories about the squirrel's unique coloration. A dye job seems the likely culprit, whether from the squirrel's nesting material or an inadvertent bath in a violet solution. Computer scientist Krish Pillai had a novel suggestion: "This is not good at all. That color looks very much like Tyrian purple. It is a natural organobromide compound seen in molluscs and rarely found in land animals. The squirrel (possibly) has too much bromide in its system."
Leaving aside that Tyrian purple (produced by a particular class of marine snail and to the best of my knowledge and research abilities by no mammal) is a much redder color, this assertion is roughly equivalent to saying that if I eat too much chloride, say from table salt, my body could start synthesizing Splenda, an organochloride. No, just, no.
Pillai is apparently extrapolating from reports that bromide (bromine anion - Br-) has been found contaminating wells near fracking sites. Calcium bromide is used in drilling fluids to increase density, by some estimates 20% of the bromine used in the US ends up in "clear brine fluids" — mixtures of various bromides. But it is a long way from bromine ions to 6,6′-dibromoindigo along very specific biochemical pathways. Which squirrels don't have. Or humans. (What can and does happen is that the bromide reacts with various chlorine compounds used in water purification to form organohalides, which aren't healthy to ingest....)
It's worth noting that direct ingestion of dyes can have interesting effects on pigmentation. Flamingos get their characteristic color from ingesting shrimp pigment, and you can change the color of a canary's feathers by feeding it paprika. Humans who eat too many carrots can develop carotenemia — they turn orange. These processes are reversible, stop eating the shrimp or carrots and feather or skin return to their normal coloration. Unfortunately consuming silver or gold can produce a permanent change in skin coloration, as in argyria.