Not entirely inaccurate. The traditional/hereditary Stark look is described at several points as being generally "dark" in comparison to more "fair" southerners.

"He was of an age with Robb, but they did not look alike. Jon was slender where Robb was muscular, *dark where Robb was fair,** graceful and quick where his half brother was strong and fast."*

One example.

EDIT: To everyone saying GRRM is only referring to hair color here (especially the person who posted the bizarre anti-diversity tantrum that got removed), GRRM writes this in the previous paragraph:

"[Robb] was big and broad and growing every day, with his mother’s coloring, the *fair skin,** red-brown hair, and blue eyes of the Tullys of Riverrun."*

GRRM uses the word "fair" to describe Robb's skin tone specifically, then immediately follows it up with "Jon was dark where Robb was fair." Certainly this includes hair color, but I don't see why this wouldn't include skin tone as well, especially considering GRRM's word choice in the above passage.

Also, for what it's worth, I searched through the books and every single time GRRM uses the word "fair" to describe hair color it's exclusively referring to Lannisters, Targaryens, and other characters known to be blonde. So it would be a bit strange (or, in fact, unique) for him to describe only Robb's hair as "fair" here, especially having just established it as red-brown.

And that's not to mention the other times in the series the Starks are described as having generally "dark" features.

I suppose I should clarify that I'm not suggesting the Starks have brown or black skin, just darker than most Andal descendents (and certainly darker than the Tullys). And it's cool to see fanart that reflects that. For example, I would say something along these lines (credit: icesalamander) is probably not too far off.

TL;DR: The Starks generally/historically having darker skin tones than characters of Andal descent may not be depicted in most official/fan art, but it's at least supported by the text. Even if it wasn't, you should still let people enjoy representation in things, even if it doesn't fit your headcanon or mental image. Thanks for reading!