I’d call that a “private cloud” and I think that’s the actual term for it. You can run a private cloud on bare metal, and if you are, then you can (as in physically able to) have control over things. If you have network cards with timestamp support, you can use PTP, or any number of things. If your org doesn’t support that, that doesn’t mean it isn’t a possibility, it just means you need to find someone else to ask.