Yes in theory the CEO reports to the board and the board reports to shareholders. In reality shareholders have zero say over what the CEO does, regardless of the share voting structure. They get the chance once a year to rubber-stamp the CEO's board nominations and that's it.

The exception is activist shareholders who acquire enough stock to get a board seat and then start agitating for change. They tend to be short-term players: once whatever merger or spinoff or dividend they were agitating for happens they move on to the next company.