I don't think anyone in the container dev community thinks that containers means LXC only. Even back in 2013, docker's front end api was designed to support other runtimes such as VMs and chroot. Perhaps this is a marketing story gone awry?
They've been using libcontainer and then moved to runC (which is effectively a standard-compliant wrapper around libcontainer) since before 1.0. LXC was only used in the early history of Docker, and it was pretty bad to be quite honest (it's better now but there's no chance Docker will switch back).
