I think this is what happened:
My goal is to have what @rubydoob suggests: to have multiple containers running on the same host. However, I wanted the host to be a Docker container.
I’m on Windows at work. I am impressed with how boot2docker performs. However, I was leery of basing a new environment on whatever boot2docker is (a barebones Virtualbox Linux VM?). I was afraid of gotchas that might exist due to it not being a full-blown Linux host. So, I thought the next best thing would be to create a Linux environment for myself based on an official Ubuntu image for Docker.
If there’s some theoretical reason why the nested container thing won’t work, then I’m fine with resigning myself to putting my multiple containers on the boot2docker environment. I won’t love it as much as I would love the nested containers! But if it works, I’ll get over it soon enough.
BTW, my use case right now was to run multiple standalone Discourse containers with an Apache proxy in front of them all.