How can Virtual Box be setup on kvm but not on xen if both are hypervisors?

While installing Virtual Box on my VM which is on xen hypervisor, I got an error as "Running VirtualBox in a Xen environment is not supported" which is ok as Virtual Box is not built for that support but installing Virtual Box on VM on kvm hypervisor seems to be working fine and all. So my question is since we need to run virtualbox hypervisor on a OS which is installed on bare metal, we cannot install a hypervisor over a virtual machine as the first thing virtualbox will do is to check if the processor have bit enabled supporting hw virtualisation. So how is it running on kvm first of all and is there something very basic that I am missing?

Output of virt-what on two systems are-

kvm

and

xenxen-hvm