Could it be that the virtualization layer does something with docker?
First of all. Docker is -not- virtualisation. It's -containerization-. Effectively namespacing and little else.
In Linux namespaces are hierarchal, I can arrange them in a tree. Where at the top namespace A can have 2 sub-namespaces B and C. A can see the process table of B and C, but B and C can only see their respective process tables. This is called pid name spacing.
Full containerisation on Linux actually requires a bunch of different namespacing, firstly the pid namespaces above but also uids, network (yes, in Docker your container has a fully namespaced network stack in including it's own (multiple!) route tables and adapters) and also device/filesystem etc.
The key take away here is NOTHING is being virtualised, we are simply only showing a section of the system to each process depending on it's position in the namespace hierarchy. What this means is Docker (well really Linux.. Docker is just glue that calls this functionality up) is just.. Linux. Nothing fancy and definitely nothing KVM/Xen/VMWare would be able to influence.
The droplet itself is virtualized.