I could see it being natural within the turks since they have less dominate hair color genes (browns and other lighter colors are more common).
Valid points but the important point in this case is that gene's origin is specifically from ireland. So naturally as with any gene it is highly concentration in and near ireland and becomes statistically more rare the farther out you go.
So while they are absolutely able to carry the gene they are unlikely to have it for that reason, and even they do it is unlikely to actually express itself because dominant genes mast it, as dominant genes do.
Red hair isnt a gene for the lack of melanin, that would be albinoism and that looks very different.