Totally correct -- In our data center, and many of the universities that we work with, will have a right hand (RH) and left hand (LH) power feed for a dual PDU server, switch, router, console server, etc. You will typically run a power bar on the right and left hand side of the rack and wire then accordingly. You will have dedicated beakers, panels, UPS, and generator, etc for the RH/LH side. If you ever need to service a panel, then you can safely cut power knowing that everything will still be powered by its partner. This happens once and a while and allows you breathing room if you need to replace a breaker or a power feed fails. We also test our generators on a monthly cycle to test for failures.
I also wanted to address you point about batteries. We have a device on each battery that monitors it's state. So we can find faults before they cause the entire UPS to fail.