The article didn't say much at all and it didn't say that everyone with PTSD will be denied a firearm. It didn't link one specific instance where this has happened and it also didn't say which kinds of firearms, it mentioned something about the Brady Handgun Bill, so maybe they can't own a handgun
There are different levels of PTSD. Anyone that has been in a bad car wreck or witnessed something bad could likely have some level of PTSD.