@InfraBlue,
Sorry Infra, I don't mean to tread on any toes here, but the context is broader than these verses alone.
In the 88th Psalm, David was troubled, his esteem was low, he feared his worth to God was akin to that of the sons of Korah. He spoke of them in verse 5 as "the slain that lie in the grave, whom thou rememberest no more: and they are cut off from thy hand"
So David suggested they had been Forgotten, and that they would not receive anything more from God.
in this context, verse 11 does not talk of the dead as forgetting. rather it he calls it the land of forgetfulness (or oblivion). But in line with verse 5 it is God who does the forgetting of that place.
That is merely how I read the text. I lead with the caveat that I have been wrong before.