For instance, Zuckerberg controls Facebook. He can not decide to use all Facebook's cash as his own personal bonus. That is because it's a clear violation of his fiduciary responsibilities to minority shareholders.
Minority shareholders have a right not to be screwed, though it is VERY difficult to establish misconduct in private companies.
If you have to break a tie, then you aren't a controlling shareholder. The idea behind controlling shareholding is that as long as you follow your duties to the minority you can install whoever you want (perhaps yourself) on the board, the board can then install whoever they want as CEO (perhaps yourself)
These things get really murky in private companies where the board, controlling interest, and CEO are shared by one individual.
It appears that Systrom and Mike Krieger (the other cofounder) together held a majority stake. Assuming the two of them decided to accept the Facebook deal, then they are indeed acting in the best interests of the majority of shareholders, no?
Why do things get murky when the CEO/board/controlling interest is the same? They started and built the company, and structured their funding deals such that they were able to keep majority control wrt voting rights. If they want to screw over the minority shareholders, I think that's pretty lame, but that should be their prerogative.
The law doesn't really give you blanket approval to do that, though. There are a lot of legal ways to screw over minority shareholders, but lots that aren't. When you sell part of your company, you agree to be bound by certain responsibilities to those minority owners. If you don't like those aspects of contract law, and want to do whatever you want without obligations to other co-owners, you need to keep 100% ownership.
In such a scenario you end up with a boilerplate contract that any right-thinking investor will insist on, just to protect themselves in such a scenario.
Basically, company law has simply declared that those clauses are there by default.