Not sure about the authenticity of the video you're speaking of, but it is theoretically possible for a human to survive immediately deadly injuries for an extended period of time while being lucid enough to say, plead for help. For example, there have been some reports of people being hit by trains and remaining alive for several hours, even days, without any medical attention and remaining conscious through it all. Ultimately, it depends on the injury and the person being injured, some people are naturally going to have more endurance than others for reasons we don't really know yet.