The sprites are weirdly-inconsistent when it comes to skin-colour. For example: in their in-game sprites, the Doctor and Jenka are the same colour as Sue, yet their facepics depict them as being closer to Momorin and Kazuma.
If I had to read between the lines... maybe it's not just that Sue is tanned - but that the others are pale. Think about it: they're a bunch of scientists who probably coop themselves up in labs all day, Sue isn't - she's just a kid that was brought along for some reason. Considering how energetic she is (navigating the Egg Corridor alone, claiming to know how to fight, and leading Quote around as they escape the falling island), she might be the outdoors-y type, lining-up with what Xemous said about sporty characters being depicted as darker in Japanese media.
For a less in-universe explanation - the presence of unused pale and dark-skinned human Sue sprites in the transformed Sue/Misery spritesheet might mean that Pixel was undecided on what human Sue was meant to look like in the first place, so he experimented with it, and then settled on a darker colour-scheme so that the transformed Sue sprites had a bit more contrast to them between her fur and her skin. With the lighter colours, they blend together.