That logic doesn't hold up. If the box doesn't respond, reboot. If it does respond though, then it's highly probable that a reboot isn't needed right that instant, and it can be delayed.
You know for a fact that it would not respond to whether it was recording or not? One of my boxes was unresponsive this morning but I could watch programming from it via MRV in another room. They were not totally unresponsive. They kept doing stuff like recording or showing video.
There are too many variables and this was an emergency situation. Force the damned reboot. Do it at a marginally acceptable time. Since late at night is too far away, do it during the typical commercial break.
Edit to add: Maybe you thought I meant it wouldn't respond. I meant that the answer was not dependable. It may have been recording because it was supposed to or it may have been recording because it got stuck. Doubt they could ask it that.