If you take investments, your investors will most likely own shares of the company (except in specific early-stage scenarios like YC's SAFE). Sometimes major investors will have board seats or voting shares. This happens in normal private companies, not just public ones.

Still has private investors it can't ignore, until it can buy them out, but it can't do that until it starts turning over a profit. Even then it may not be able to get rid of them if they own enough of a share.