Your theory is that emergency room workers would think "make sure patient X gets operation Y" so unimportant that they'd just leave it off the board? I have more faith in them than that.

There is no job where all work is equally important, where all ideas are equally good. Even in emergency rooms, where triage is a vital concept. I think it's ok if finding a new poster for the break room gets dropped because there's too much work treating patients right now.