That's just our docs being unclear :) You can run docker on debian wheezy, no problem.

Docker is currently easier to run on certain distros than others. But it's not because it's distro-specific. It's because it has kernel requirements which are more easily met on certain distros than others. Those requirements are described at http://docs.docker.io/en/latest/installation/kernel/ (short version: aufs + lxc + (<=2.6 OR >=3.8))