  In recent work by Zimmer it was proved that if $\Omega\subset\mathbb C^n$ is
a bounded convex domain with $C^\infty$-smooth boundary, then $\Omega$ is
strictly pseudoconvex provided that the squeezing function approaches one as
one approaches the boundary. We show that this result fails if $\Omega$ is only
assumed to be $C^2$-smooth.
