Direct owner is a term that basically means someone who has ownership, beneficial ownership, voting rights, or rights to sell. Sam Altman was that. He was also an indirect owner through OpenAI Startup Fund GP I, which is the other entity you are talking about. You don't need either to be GP, though it can make things simpler. As far as the bundle of rights in ownership is concerned, yes, he did own the fund.
Anyway, the obfuscation bit is from the filings with the state, not so much the SEC - there for a period of time OpenAI Startup Fund GP I was managed by Vespers, Inc. and had a bunch of registrants with fake names and fake directors and board members on the filings, all with the same address, an affordable housing unit in Santa Ana.
The statement that he owned 75% of the fund is deliberately misleading. That he was in control of an entity that acted as the GP of a partnership means "he was acting as GP". But, that doesn't sound as nefarious, and it doesn't sound so sensational, and that's why it's not being said that way.
The only way to know if something shady is going on is to read the partnership agreement of the actual fund. That's where the rubber meets the road.