No, you're not a bad person. Based on what you said, I kinda doubt her diagnosis. "Being picked on" as a kid doesn't cause PTSD. Being bullied as a kid can cause PTSD. Yes, there is a difference! I think she's more in the "being picked on" category. Nobody who was traumatized as a kid says "I guess it was bad". Most of us are like "eff that bully!"
I disclosed my diagnosis to a friend and she gave me an enthusiastic "ME TOO!' I literally wanted to punch her because I felt completely invalidated.
PTSD isn't a bonding factor. I am very much in the "if you have PTSD, too, then I cannot be your friend" camp. Ok, this sounds harsh, but it is actually a boundary I have set up for myself in order to protect my own healing. That friend with PTSD? Well, we're still friends, albeit on a very distant level. My aunt also has PTSD and she'll always be family to me. What I mean is that I don't seek out new relationships with sufferers as PTSD isn't a healthy basis for a relationship for me at this point, nor do I think it would ever be. There is too much of a risk of me triggering someone else, or of them triggering me. Oddly though, I can have friends who have anxiety, just not PTSD. Go figure.