I'm not sure where some of you get your ideas.  But backing off metaphorically means not pushing further into the area to have him pop more shots at their heads.  It means backing down a bit, not leaving the area, not retreating from the location.  Just backing up so the guy doesn't have a good bead on your head would be a freaking start.  The issue is that mediating costs money.  The longer they attempt to wait him out the more money it costs the city.  So negotiators are taught to try and talk suspects down quickly if possible but they will always make an attempt to take a suspect down whatever works fastest. If they think there's an entry point where they won't get killed they'll take the risk and it's possible he's going to get killed. 

Longest standoff I've seen in anchorage ever to be honest.