I don't 100% know if the containers themselves are hosted by Hetzner or not, but Hetzner is more of a budget provider than something you host production sites on.
I've heard many mixed review about their network and mostly their support which isn't up to scratch. We'll see what happens but from what I see, if someone decides to abuse the service, Hetzner might just take down the whole server without warning just like OVH do.
http://www.hetzner.de/en/hosting/produkte_rootserver/px120ss... (I'm guessing they are using something similar to this).It's a pretty powerful and cheap server but if you search hard enough you can find something equivalent in the States for around the same price.
If you need real HA you should perhaps use more than one provider anyway. Or what are your recommendations?
Since Docker is still in beta, it's not production ready yet anyways. Docker could still go through a lot of changes between now and 1.0.
ETA: Whoops, I got the pricing wrong. It's $5 per instance. I was thinking you would get 1GB of RAM and 20GB of space to run as many containers as you like. That makes it not as cheap as I was originally thinking.