Is an OS just the kernel? Then yes, Docker doesn't contain an OS.
Is the OS the userland? E.g. the init process + the shell + the C library + other runtimes? Then most Docker containers actually do contain an OS. Yes you can get rid of most of them by making static binaries, but why would you want to? Making static binaries with anything besides Go is a pain, and good luck trying to statically link MySQL or Redis into your binary.
Lets take sshd for example, you would need to create a skeleton directory structure, /bin, /dev, /lib, etc in your rootfs container, have /bin/bash, a whack of /libs, some /dev devices, and then your sshd application. So an extremely minimalistic rootfs with only the sshd requirements. You could find these my running 'lsof -p `pidof sshd`' , maybe 'ldd /usr/sbin/sshd' (and all their dependencies) too, which quickly snowballs.
Hopefully this explains where I was going with that. Also, this is not a simple task to try and strip off these services into self contained entities. There are lots of hidden issues, like how do we handle logging? Should the container have syslog too? So, there is work that needs to happen, I just like the idea of not running a full fledged OS in a container.
Your original comment talks about how long LXC has existed but AUFS is one key component of Docker that became part of mainline Linux much more recently.
AUFS is not part of mainline kernel. Many distros include it (Debian, Ubuntu). But some don't (Fedora).