Yeah but it's possible that Destiny's universe has it's own version of the forerunners, I believe it's pretty well established that there's a miltiverse in destiny's universe.
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The forerunners network spanned starsystems from what I understand which is the same thing as the ones from the grimiore, the forerunners in halo could manipulate matter....just like the ones in the grimiore. I'm pretty sure Oryx exterminating the forerunners was done on purpose in the grimiore as a nod or at least a reference to halo
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You're right they are not, they were but not anymore because oryx killed them. But if you're talking like copyright wise or something like that then yeah there's a reason they weren't directly called forerunners. But I feel like they definitely intended to write it in as some sort of easter egg which I think is cool.