Correct. Index funds are owned by people. For example, I have invested a large chunk of my retirement savings in an S&P 500 indexed fund (as many, many other people do). Whatever stocks the S&P 500 list, are what I end up owning; if I don't want to own one of those, I have to either roll that money into a different fund (which IIRC has limits, can't do that too often without tax consequences) or take the money out (and pay a tax penalty for withdrawing it before retirement).

So whether the index funds do or don't buy a certain stock has direct implications for real, non-millionaire, people.

No, they're just owned by people. Most of whom aren't billionaires.