I feel like you're being deliberately pedantic in a general sense and ignoring the terms of art here.
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.