That may be true in many companies, but venture capital funded companies almost always have something called a "Voting Agreement". I pulled a random one from my folder of docs, it is below. The upshot, if you are not used to reading these, is that all of the shareholders signed an agreement that says they will vote their shares to elect certain directors. In the absence of an agreement like this you are right, the board could fire the CEO but the majority shareholder could fire the board. But, again, every equity round from a VC that I have seen in the last 25 years (and, I assume, longer, but that's as far back as my personal knowledge goes) has a Voting Agreement in some shape or form.
Actual text from a Voting Agreement:
"NOW, THEREFORE, the parties agree as follows:
1. Voting Provisions Regarding Board of Directors.
1.1 Board Composition. Each Stockholder agrees to vote, or cause to be voted, all securities of the Company the holders of which are entitled to vote for members of the Board, including without limitation, all shares of Common Stock, Series A Preferred Stock, by whatever name called, now owned or subsequently acquired by a Stockholder, however acquired, whether through stock splits, stock dividends, reclassifications, recapitalizations, similar events or otherwise (“Shares”) owned by such Stockholder, or over which such Stockholder has voting control, from time to time and at all times, in whatever manner as shall be necessary to ensure that at each annual or special meeting of stockholders at which an election of directors is held or pursuant to any written consent of the stockholders, the following persons shall be elected to the Board:
(a) For so long as there remain outstanding not less than 200,000 shares of Series A Preferred Stock (subject to appropriate adjustment in the event of any stock dividend, stock split, combination or other similar recapitalization with respect to the Series A Preferred Stock), one (1) individual designated by the holders of a majority of the shares of Series A Preferred Stock then outstanding, which individual shall initially be Jerry Neumann (such director being the director defined as the Series A Directors in the Restated Certificate); and
(b) Two (2) individuals designated by the Key Holders who are at such time providing services to the Company as an officer, director, employee, consultant or advisor holding a majority of the Shares then held by such Key Holders (each such director being one of the directors defined as a Common Director in the Restated Certificate);"
etc. etc.