Your reply primarily addresses architecture support and the implications for pre-built payloads. But I think a more important concern is the fragmentation that would result if Docker attempted to natively support other operating systems. Consider that practically every Dockerfile starts with a Linux distro, and includes commands specific to that distro (e.g. installing packages with apt). Everybody assumes that the payload is Linux-based, and it all just works. How would it work if Docker also supported FreeBSD jails, Illumos zones, or whatever other options are up for consideration? Would the public registry of Docker images now be fragmented along OS lines? Or would Docker try to automagically smooth over the fragmentation by firing up VMs when the host and container operating systems don't match? In the latter case, would every Docker installation then require a working hypervisor?

Considering that the overwhelming majority of Unix servers are running Linux, I think it's better to say that Docker is Linux-based, end of discussion.