Actually, I just did it myself, and I'm almost certain it's purple, just in the shade. If you use the eye dropper to select part of her hair, then click the box with the color you just selected, it will give you the stats of her hair and allow you to adjust the Hue, Saturation, and Lightning
I tried multiple places on her hair, and in most of them you could plainly see that turning up the Lightning showed it as clearly purple (even the really dark "pigtails" part turns purple). The only place that didn't was near the bottom closest to her cheek, where it showed up as gray instead. I think that can be explained as that part of the hair having a glare that's reflecting the light though.
Edit: To clarify, use the "Colorpicker" tool and click some place on her hair. On the menu a few icons below the Colorpicker tool is a colored box tha says "Set Main Color" if you hover your mouse over it. This box will change colors to match the color of whatever you click with the Colorpicker.
After clicking her hair, left click the colored box. This will bring up a lot information about that specific color. Of note, there are 3 sliders present labeled H, S, and L (for Hue, Saturation, and Lightness). In almost all cases (except the glare around her ribbon near her cheek), the L slider will plainly show you that it is purple.
