Public companies can have multiple classes of stock with different voting rights. Private company can be sold.

Sure they can, but most public companies (absent places like Facebook, which IIRC has a setup which favours Zuckerberg heavily) are more susceptible to being forced to sell whether they want to or not.

Private companies (especially one's who aren't beholden to VCs or similar) have the option to say no, regardless of how much money they're offered.

I always find this language kind of interesting. Companies are inanimate entities, they can't want or not want something. When you say "they want to" or "have the option to" who do you really mean?

Pretty sure the gp is referring to employees and top management, rather than shareholders. I.e. the actual daily functioning portion of the company.