Since the Trinity* all formed in '68, it's tough to say if any person or band really invented metal. Of the originals, I think Black Sabbath sort of took ownership in the earlier years, maybe in part because Page was so obsessed with fame and wealth and in part because Sabbath was really into building their myth. It would be easy to argue that the trinity were all late to the game, since examples were out there before '68, but they weren't fully formed visions. Once the first Sabbath LP was out, it was difficult to say it wasn't part of the definition of a genre.
The first interview I ever saw that talked about heavy metal was with Page in '67, towards the end of his involvement with they Yardbirds. Page had contractual obligations and with the Yardbirds coming to an end, he had to get another band together - quickly. In the interview, he talked about his vision for heavy metal, with the loud and the quiet, the shadow and the bright, etc. I read that Page later credited Burroughs with the phrase, copped from The Soft Machine, by way of Steppenwolf's Born to Be Wild.
I'd totally believe that Sabbath and Purple ignored the others and did their own thing because that's where rock was headed. The prog side, psychedelic blues, hard rock - they all came together with the advent of putting way more power and quality into PAs and having crews and players that understood the importance of having great live sound. Zappa, the Dead, Hendrix, Cream and others all invested in their live sound in $ and effort, then all of live music benefitted. I don't think metal could have made it with the PAs of '65 and earlier.
*: Led Zeppelin, Black Sabbath, Deep Purple