I think there are many contributing aspects to the whiteness of titanium white. I think it is difficult to cover all of them in a single answer. You already have a very nice answer from Stefan Bischof who emphasizes the importance of the BRDF in this case.
I want to mention another aspect. The refraction index is obtained as
$n = \sqrt{\mu_r\epsilon_r}$
where $\mu_r$ is the relative magnetic permeability and $\epsilon_r$ is the relative electric permitivity or dielectric constant. These quantities are in fact not so constant but functions of the frequency $\omega$ of the electromagnetic wave. Let us assume that the relative magnetic permeability is 1. This should be realistic for nonmagnetic materials. $\epsilon_r$ also is not a real function, but a complex function $\epsilon_r(\omega) = \epsilon_r^{'}(\omega) + i \epsilon_r^{''}(\omega)$. As a consequence also the refraction index is a complex function.
The important thing in this description is that the absorption of the electromagnetic wave in the material is determined by the imaginary part of the dielectric function. For the whole frequency range of the visible light this is obviously rather small for TiO2.