some dogs have black pigment around their eyes, some do not.
sometimes my dogs have circles of wetness around their eyes, like when I take
too many flash photos; but they each have black pigment like eyeliner

just like noses that vary from light brown, pink, black and so on--the area
around the eyes differs from dog to dog. Tear stains are a totally different
issue and you can Google that subject for more info or search here on Chi Ppl.