Why do some host volumes in Docker containers give the error "too many levels of symbolic links"?

This is caused by directories not being automounted when the container is run. I had thought that /usr/groups/thing was the automount point, but evidently the sub-directories are auto-mounted individually. The solution is to make sure each one is mounted before entering the container:

$ (cd /usr/groups/thing/foo; cd /usr/groups/thing/bar)
$ docker run -v /usr/groups/thing -ti imagename /bin/bash
# ls /usr/groups/thing/bar
d e f