My guess is that the majority stick around, especially if it's someone who knew the victim and would be missed. Also, just think about the statistics of killers who return to the scene of the crime or insert themselves into the investigation.
Having said that, I do find the comments made by LF, who says she went fishing the night JC died, to be interesting. She either doesn't have a filter or she was nervous and just couldn't stop talking. And I personally think it's strange that she went to the scene and gave an interview. She acted like she knew JC well but also said that she was really friends with JC's older sister. Then she talks about JC's visits to the Sonic and that she called her "my Sonic baby". Then she makes fun of JC always messing with her eyelashes. I don't know. It is probably nothing but I think she gave way too much detail about how she found out JC had been killed. Then she goes with her sister and their kids to the scene and gives an interview including the information that she had driven past that area the night before. It just makes me wonder what her intentions were.
Placing oneself at the scene of a crime does have a way of capturing my attention.