You know this actually does make sense. He's never been a ginger, but has always wanted to be. Poor old Doctor, that's what hair dye is for. In all seriousness, what if there's a real Doctor and he's actually a ginger.
"You’re always gonna be afraid, even if you learn to hide it. Fear is like… a companion. A constant companion, always there. Because fear can bring us together. Fear can bring you home… Fear makes companions of us all.
"The way I see it, every life is a pile of good things and bad things. The good things don’t always soften the bad things, but vice versa, the bad things don’t always spoil the good things and make them unimportant.” -Doctor Who