vegans can eat traces of milk?

So in my quest for dairy-free chocolate, I checked out the vegan chocolate section of my local wegmans.  It was almost a no-go, only one of my 7 options was really dairy-free.  All of the rest ‘might’ have contained traces of milk.

I’m no vegan, so I don’t really know the rules, but I thought they had some rule against no-animal-product eating.  And, well, traces of milk certainly sounds like an animal by-product to me.  Also, from what I understand, it’s a  whole philosophy of life, not just a way of eating.  So it would seem to me that a vegan would only want to buy products from companies who also espoused that way of life – or at the very least, took it seriously enough to devote a wing of their factory to vegan-only.

But, what do I know, I’m not a vegan.  It sure would make my 10-day dairy free challenge go a lot easier if I could trust that vegan=no dairy.