Singular del Pezzo surfaces over finite fields

Abstract: If $X$ is a singular del Pezzo surface of degree $d$ over a finite field $\mathbb{F}{q}$ with only rational double point singularities, does there always exist a smooth $\mathbb{F}{q}$-point on $X$? We show that this is true for $d\geq 3$ and give counterexamples in the case of $d=2$.