Exactly. I know the three guys that coined the term Grindcore personally. Ive been lucky enough to get a first hand 'This is how it went' lecture on it. It has absolutely nothing to do with 'Early Black Metal'. Wouldnt that be like Bathory and possibly Venom? Sorry but Napalm Death were influenced highly by the likes of Crass, Rudimentary Peni, The Amebix, and Discharge. Put them in the Punk tree or it aint right. The only one of the three that was even remotely 'metal' influenced, aside from a love of Black Sabbath, was Justin Broadrick and his love for Celtic Frost riffs at double speed.First, let me say that the graph you posted was neither comprehensive, nor wholly accurate by my reckoning. That aside, on to your question.
And really Black Metal sprung from Hardcore?? Ive never once in an interview ever seen Euronymous or Abbath say 'Hey we were totally inspired to burn churches and worship pagan gods thanks to Agnostic Front and The Cro Mags'! What they did was a reaction to what they thought was 'fake theatrical' american death metal. They hated and despised most american thrash/death/hardcore (even though Euronymous sold lots of it in his shop).