Many cable systems and all satellite systems have dedicated boxes that are required to get any sort of useful signal. If one's system is like that, then you can only record or live-view one thing at a time. You could bypass the DVR and watch something that doesn't require the box, but this is likely to be nearly nothing.

If you have a cable system that doesn't require a box or if for some reason you can actually receive a decent number of channels at good quality over the air, then you can certainly view something other than what the DVR is viewing, but in my experience, such setups have always been uncommon and are only getting rarer.