Have you considered that maybe he was lying about PTSD? I have been around drug users enough to know that what you described might also have been a result from PCP or Methamphetamine use. It even makes sense if the neighborhood is a non-wealthy one. The main red flags to me are that his hands are bloodied AND he climbed a tall barbed wire fence. Users of these drugs usually have quieted pain receptors and are too amped up to feel any pain. And are also easily angered by loud noises and disturbances.
So what I think may have happened is: A man on PCP or some other violent drug got irrationally angry from hearing music, punched some stuff and climbed a barbed wire fence (without feeling any pain) and totally raged out on you. It makes sense for him to say that he has PTSD to "explain" his rage. But also he may have PTSD AND been on drugs, you'd never know.
It very well could be both. Self-medicating is all-too-common for people with mental issues, and PTSD is certainly no exception. Alcoholism, drug use, etc, can be ways people cope with or numb their mental wounds.