Sociopaths and psychopaths are born that way. One of the biggest red flags is starting fires, which OP notes has occurred. These personalities will also lie with no regard to consequence. It is possible this child believes a group home or foster home will be a better experience for her and her mom is saying, well then let’s send you to one, no need to keep making false accusations, try it. Obviously moms post history shows she is trying to get help.

IDK if her kids is a sociopath, borderline, or something else.

But speaking to your point- there are personalities that lie and hurt people with no care to what that does to them. It does happen.