When I was in one of the vSphere training classes the instructor informed us that the hypervisor is completely homegrown and that only the Management Console (which is a VM that provides CLI access) runs on top of a Linux kernel.
Not saying that VMware Inc are wrong, but Linux runs VMkernel. VMkernel may them 'subsume' its parent kernel somehow but I'm not sure how they'd accomplish this, nor do VMware like talking about how this is achieved.