It's true, a direct link hasn't been proven, and I was debating even mentioning that. Obviously that specific tendency alone isn't indicative of a homicidal individual. But I would speculate that it has something to do with dysfunction/dysregulation of the autonomic nervous system.
Yes, but that is the absence of evidence, commonly called on when the science hasn't been done.
If a theory/hypothesis remains not proven once the science has been repeatedly done in numerous attempts to prove it, very often it does mean it is wrong.
It still seems like it could be correlated, but it shouldn't be used as a diagnostic measure or taken as a sign of something. It's more likely to be a sign of abusive parenting, but abusive parenting is also correlated with the psychopath behavior so it all ends up being correlated with each other.
The replication crisis was recently discovered; this does not mean older science does not have the same challenges. Generally the problems that led to the replication crisis are worse the further back you go in time