I'll tell ya, I've chewed tobacco that'll stain your fingers, lips, teeth and anything it comes in contact with.
I'm not saying that the wrappers are dyed or not, because I don't know.
What I do know is that tobacco gives off colored juice, and it'll leave it's impression on my fingers.
I do a lot of slobbering and chewing on my cigars.
A couple weeks ago I smoked an Anejo and had a hell of a mess. Into my mouth I squeezed out the juicy mess I had made. It was incredibly salty.
When I spit it out, it was almost black. The stain on the sidewalk will probably last forever and my fingers were stained.
I don't want think that Anejo's are dyed, ya know?
I guess my point is that this sounds more like a conspirary theory than fact to me, and that some tobacco makes some serious "dye" of it's own.
It doesn't matter one way or another to me, though. I'd rather not smoke dye, so I'll probably stay away from sticks that I know are dyed if I know before I buy them.