The problem is that there can be any number of non-voluntary physical actions following a head shot, including contractions of muscle groups.
The problem is that you cannot predict what if any involuntary reactions will or will not occur. So, to base not taking the shot on that is no more supported by science than not. Although it would be interesting to see if there was any data to support it (actuall incidents, not extrapolation or theory). Assuming that the BG will pull the trigger is pure speculation and there is no way to determine if he can or will. However, what you can determine is that if you let the hostage taker leave, the situation is out of your control and the odds are against your loved one's survival.