Daytona has security that walks the fence, telling people to move back as they pass. Of course, when the cars go by, fans will still run up to the fence if the guards are not there, like this lady in blue:
http://www.racerjon.com/pictures/miscshots/random/blue_shirt_lady-highlight.jpg
As the cars come down you can see in the fan-video she is running up to the fence to get closer.
Afterwards:
http://www.racerjon.com/pictures/miscshots/random/blue_shirt_lady_2.jpg
I would say there is no excuse for her behavior, and she should have known better.
also
http://www.gannett-cdn.com/media/USATODAY/USATODAY/2013/02/23/daytona_027-3_4_rx812_c608x810.jpg?a89b7f984a68464808b67913caf32c8a35d378cb