To be clear, I prefer the first interpretation, but I realize open data geeks (and those who would use the raw data if granted access) are far fewer than ML geeks (and those who enjoy the automagic suggestions) and the gap is only widening.
In the early days of Google, I assumed that to organize and make accessible meant to index and link to information presented by others - and not to ‘own’ the data.
It saddens me that that interpretation is no longer correct - and perhaps never was?
But the wording is certainly neutral on who houses and owns the data.
I'm guessing that you're right as to the early interpretation, since that's what makes sense for web search.
But other interpretations are the logical thing to think of first for some of their more recent ML-powered assist/suggest products, and the wording of the mission statement leaves product managers and architects/designers free to apply whatever interpretation makes natural sense in context.
What is Google's mission nowadays? I don't see them following a lot of "Organize the world's information and make it open". There's a ton of closed walls, they even acquired companies like freebase and then their stuff went behind closed doors.