Wrong. Two entities run everything: Blackrock and Vanguard.
http://johncbogle.com/wordpress/wp-content/uploads/2019/08/n...
(This is arguably a bad thing for long term economic health, since broad-market ETFs have a dampening effect on otherwise healthy amounts of speculation. But I think it's a far cry from saying that they "control" the market, since it's a mostly passive effect.)