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
I just ran in to this problem, and while the solution I found certainly won't be for everybody, it was a subtle part of my setup that was causing the issue.
To save space, I'd moved the Docker directory from my %APPDATA% directory on my SSD, to my much larger HDD, and setup a junction to point to it in its new home.
I eventually remembered that this was the case, and moved the directory back. Restarted my PC, and the error stopped occurring.
Like I say, that's pretty niche, but it solved it for me.