Don't apply rmtree(), which will gleefully remove an entire subtree,
and don't even apply unlink() unless it's symlink or a directory,
the only things that we expect to find.
Amit Kapila, with minor tweaks by me, per extensive discussions
involving Andrew Dunstan, Fujii Masao, and Heikki Linnakangas,
at least some of whom also reviewed the code.
8f15f74a44