The company still has a fiduciary duty to all shareholders, not just majority owners. A smaller shareholder could still argue in court that management is breaching those responsibilities.

That said (and IANAL), at least the couple suits I'm familiar with in this area have to do with minority shareholders arguing some decision was made to benefit majority owners at the expensive of minority shareholders. It's much, much more difficult to just argue "bad decision making" if all shareholders are affected equally.