Let's start with Apple
Apple is a publicly traded company. Vanguard owns about 7-8% of the shares. They are the largest minority shareholder. While that gives them some weight to sling around it does not give them dictate rights to Apple or the board. Blackrock and Berkshire Hathaway would have something to say to that as well. They are the 2nd and 3rd largest minority owners respectively.
Apple's directors must have majority votes from the shareholders. The board has oversight of the company to ensure it's delivering its mandate to the shareholders.
Vanguard is owned by its funds and is therefore owned by its own customers.
In other words red-text-anon, shareholders own Apple and fund investors own Vanguard. All public. All accountable to the shareholders and owners.