This is not accurate. I am currently running an Ubuntu Docker host, but a CentOS 6.4 based container, a Gentoo container, and a busybox container.
As stated elsewhere in this thread, which I encourage you to read, Docker aims to solve problems that exist in container technologies across kernels by taking advantage of their strengths (Docker does not aim to replace libvirt/lxc/jails/zones) but instead to build abstractions on top of them for better building, management, discovery, and scale.