1) Docker 0.7 will run on vanilla kernels out of the box. This means virtually all distros will be supported. It also means wider support for hosting providers which don't allow custom kernels (Google Compute Engine for example).
2) Future versions of Docker will optionally support some of the technology used by Red Hat - most prominently libvirt-lxc and selinux.
The more places you can use Docker, the more useful it is :) So we have no intention of locking it into a single distro or paas.
[1] https://fedoraproject.org/wiki/Features/SVirt_Mandatory_Acce...
What I mean, regardless of how we actually implement, is having an elegant way to deploy containers in environments where the sysadmin relies on SELinux contexts and labels to implement security.
This is basically just expanding our current abilities to include areas where we didn't have great support before.
The goal is to have Docker running on all linux platforms, so that everyone can use it regardless of their distro choice.