`\cellcolor` in tabular inside tabular

[tp971]

When using \cellcolor in a tabular that is inside another tabular, it colors the outer instead of the inner cell:

\documentclass{article}

\usepackage{colortbl}

\begin{document}

\begin{tabular}{ccc}
a & b & c \\
d & \begin{tabular}{ccc}
    e & e & e \\
    e & \cellcolor{red}e & e \\
    e & e & e
\end{tabular} & f \\
g & h & i
\end{tabular}

\end{document}