This is an incredibly dangerous assumption to make and should not be done based on a few paragraphs of second-hand statements on the internet.

Is it more dangerous than labeling the girl a psychopath/sociopath even though the grandmother is just some ole biddy and not a trained expert?

An expert would also know that children are not diagnosed with antisocial personality disorder anyway, and for good reasons. I’m guessing that granny isn’t familiar with conduct disorder, and even if she was, unable to distinguish it from more likely issues plaguing the kid. Children can be sociopathic, any parent knows this, but that doesn’t make them sociopaths. Children are not fully developed, and it’s dsngerous and unethical to casually label them with a personality disorder.

I think your "diagnoses" (are you a medical professional?) of emotional abuse - along with the grandmother's diagnosis of sociopathy - are on very shaky ground. The girl may just have a temper. Many children outgrow this.

I also immediately jumped to this conclusion. I was emotionally (and physically) abused myself, so I believe I have some insight.