The example given was a car accident. Should you come across an accident and are the first or one of the first on the scene, the worst thing you can say to anyone is "You will be OK". The philosophy behind this is that the person you are talking to may be in extreme pain and confusion. They believe the worse about what may/will happen to them. With a stranger telling them that they will be OK, you have set yourself up to not be credible to them. They will not believe anything else you may tell them as they may not believe that they will indeed be OK.
What was suggested that you say was "OK, the worst is over, now we need to get you taken care of". The philosophy for this is that you are helping them to realize that indeed the worst has happen, they have already been in the accident! From now on things will progress towards an improved condition/situation.
Food for thought...