  A topological space $X$ is strongly $D$ if for any neighbourhood assignment
$\{U_x:x\in X\}$, there is a $D\subseteq X$ such that $\{U_x:x\in D\}$ covers
$X$ and $D$ is locally finite in the topology generated by $\{U_x:x\in X\}$. We
prove that $\diamondsuit$ implies that there is an $HFC_w$ space in
$2^{\omega_1}$ (hence 0-dimensional, Hausdorff and hereditarily Lindel\"of)
which is not strongly $D$. We also show that any $HFC$ space $X$ is dually
discrete and if additionally, countable sets have Menger closure then $X$ is a
$D$-space.
