My OpenVZ (debian) host environment has only the minimal packages installed. Now I was irritated to see a mysqld process in top when the mysql package is installed and running only in one container. So I killed it and saw the service down in the container. I can start it there again and everything is fine. But - was it not the idea of a virtual environment to separate the OS instances and their processes between host and clients?
OpenVZ is not a virtualization solution - it's a container solution. There's only a single kernel instance, and that kernel knows about all processes running on the system, regardless of whether or not they're in a container.
For this reason and many others, OpenVZ is not well-liked among professional sysadmins - it's a lowest-common-denominator solution that is tailored to webhosting companies.
If you want true virtualization, look into something like KVM, VMware ESXi, Xen, etc.
Think about OpenVZ is not a fully virtualization solution but a container virtualization one http://en.wikipedia.org/wiki/OpenVZ#OpenVZ_compared_to_other_virtualization_technologies. Its aim is to run lightweiht virtual servers with less overhead than an hypervisor.
The processes are fully separated from different OS instances (Guests) but the Host itself is a special one. You can think (simplifying really a lot) of OpenVZ as a sort of advanced chroot, rather than an alternative to VMWare, Virtualbox or Xen.