That's not accurate.

I suppose not; it's not as if they copied and pasted the jail code, merely cited it as prior art in describing their own implementation.

Nevertheless, jails have been the BSD "container story" for over fifteen years.

And, it is not a convincing one. Being old does not make it competitive.

Haven't you already disqualified yourself from being able to make that judgment? ("I've never seriously used any BSD.")

Being old does give it a long history of successful use. Jails are exactly what Docker for FreeBSD uses for its containers; I'm not sure what more you'd be looking for in a container system, if lxc is something you'll mention in a positive light.