I wonder if it's a single container, running your OS on top of theirs then. I don't see how their API would work sans both a VM and containers. Unless maybe they are supplying a fixed set of tweaked distributions.
I don't know their specific setup, but Bare Metal providers generally either netboot your image, or netboot something that copies your image to local disk, and then reboot into it. That can be automated quite far, the biggest issue is having a hardware platform that can't be permanently compromised by the running OS (e.g. on a typical x86 system, the OS could reflash the BIOS or firmware of other components)