The full quote here is「人間到る処青山有り」, which indeed comes from that 月性 guy. I suppose it would be translated as "Throughout the world there exist green hills"?the implication is it doesn't matter where you go, because there are green hills everywhere to be buried in. Of course, it seems you already gathered that much.
The partial phrase 「至る所に青山あり」 removes the "world" aspect of it, though it would still be something like "There exist graves everywhere". The initial translation appears to have been "Bound for the Graves", and I suspect the translator looked at 至る (いたる) "to reach, to arrive, etc." and 所 (ところ) "place, location" separately instead of seeing 至る所 (いたるところ) "everywhere, all over, throughout". Combining that with 青山 (せいざん) which can be translated as "grave, burial place", you can see how the translator came up with "Bound for the Graves", where "bound" is along the lines of "headed for, destined for". This translation, "Bound for the Graves", seems to have been misinterpreted into becoming "Bound to the Grave", likely because the second person believed "bound" was the past tense of "bind". And that's where we are now.
I'm not really sure how the name corresponds to the skill itself, but that's not that important.