"We have closed out our position in GME (GameStop)" isn't ambiguous.
> Why would they bother to make such statements early in the AM if they had actually closed out their shorts?
Most likely: Citadel required them to. The bailout was going to be announced. Citadel didn't want informed observers speculating on whether Citadel had just ponied up to an unhedged falling knife.
Otherwise, Melvin is a hedge fund. Its LPs are nervous, and assuring them the worst is over could sow doubt in would-be defectors. This could also be done by way of confidential notice, however, so on its own it isn't enough. The other factor is, perhaps, to get the people prank calling and such off their backs. That was a stated factor for Left at Citron.
Why would they bother to make such statements early in the AM if they had actually closed out their shorts?
They said before they do not comment on their positions. Why would they do so now if it wasn't a serious situation?