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Sam -- don't bother with eyes or teeth -- they are never white, they are light warm yellowish-red. The white part of the wristband is the only test area. When you say the white wristband is "gray" does that mean you just hovered over it with the dropper tool, or did you take the numerical readings to decide it was gray. The advice was intended for you to "click" on the white area to see if that sorted out the color, not hover.
Besides the reflected light from the yellow/green plastic, it seems your light source is a mix of fluorescent and daylight, is that right? If so, you have an almost impossible color balance situation, and the camera has done a pretty good job. If you are using LR4, you can tweak the temperature a little warmer, and you could try raising the magenta a touch. Both would be minute changes, nothing major.
If I were photographing this "for real" I'd use a flash filtered to match the predominant lighting (if not daylight) and use that for fill and to achieve color continuity to override the reflected colors as much as possible. Even without filter, the flash fill often provides a better baseline for color correction where no white or grey exists.