Good question. I'm afraid I can offer no better explanation than that precis just doesn't change when becoming an adverb.
Slightly confused about this, where is the "the?"
Would "Det är precis den samma färgen" work?
No, the word samma will never accept definiteness in what it's describing. It's an exception in that way.
Do you know if there exists a definitive list of these exceptions somewhere?
I don't know. Hopefully someone knowledgeable will provide a link somehow, or perhaps it's googleagle.