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There are asset management firms with AUM well in the trillions: https://en.wikipedia.org/wiki/List_of_asset_management_firms

That "biggest" claim is based on a Cnet article, which is based on a ZeroHedge article, and they just state it as a self-evident fact, that Bridgewater is the "biggest" hedge fund.

And it's again not clear that Braeburn is a hedge fund. (It's very composed of many smaller funds anyway, each with different risk profiles.)

That said, yes, Apple's cash is absolutely not just sitting in Tim Cook's basement.