I can't watch the video right now, I can think of a number of reasons why staying would be a good idea.
One would be preservation of evidence. Forensics will tell a story, and the one story you want it to tell is what actually happened.
When you leave the scene, there is no telling what will happen while you're not there to see it any more.
The police will conduct an investigation, which will include everything from interviews of witnesses, gathering of physical evidence, and a forensics investigation. When the evidence supports your story, that is a strong indicator that you're not lying about what happened.
If other people come in behind you and ransack/disturb the scene, maliciously or otherwise, that hurts your own story.
Now, obviously staying on the scene may not be the healthiest choice one can make. Threats to your own safety have to be taken seriously.