I haven't watched the specific programme you're talking about, but I am reasonably familiar with the genetic hypothesis. For clarity, I think you've summed it up well above (though saying it's an indisputable fact is a little early just yet - there's just compelling evidence for it), except that it doesn't account for everybody who kills, it just accounts for particular motives for killing.
In fact the context I've heard of the research wasn't on research into all killers per se - it was on psychopathy. And psychopaths, while they can be extremely dangerous and difficult to track down when they do kill (and not all do), they don't account for a particularly large portion of the murder rate.