I don't know about just as bad, but oppressed groups who've launched rebellions, even completely justified ones, have indeed become evil overnight. Look at the Haitian slave rebellions. Or more recently, jihadist groups under Assad's Syria.
You're right that this fact can be used by oppressors to justify their oppression. Not sure if that was the intent behind BioShock Infinite. I suspect not, but it's possible.
It doesn't really matter if it was the intent or not, you(Levine, not you the poster) are creating that moral equivalency by your framing combined with lack of sufficient context in the story or character.
You are removing the underlying context of oppressor and oppressed and both-sidesing them on a moral plane.
When Booker calls them "both the same" he's essentially channeling Levine's morality which boils down to seeing no difference between a person at their breaking point, stealing food to survive, and a person stealing from the hungry and destitute because they have the power to legally and physically exploit them with impunity.
To do so in a game about slavery no less, is rather grotesque.
EDIT: As for your analogy, I don't know enough about the Haitian rebellion to feel comfortable speaking, but the Jihadist groups in Syria to an extent I do. And even there you wouldn't be right in making any sort of moral equivalency. Instead, the context I would suggest is that Syria is a tragedy of history, domination and imperialism, and in that context of overwhelming domination and oppression, the only means to fight back tends to be through those that can organize, radicalize, mobilize, strategize, and physically attack back at their overwhelming oppressors. And the tragedy is that most times the only groups that find sustained success in pushing back are the ones fostered through less than ideal processes (like religious, ethnic, and nationalist radicalization, preying on the feeling of helplessness of naive and angry youth). It's not a story of the good becoming evil, it's a story of evil so overwhelming that the system it has imposed on its victims makes the privileged western concept of morality a near impossibility of remaining adhered to in rebelling against.
But what you get out of Levine is not that sort of nuance, instead what you get from him is taking that sort of tragic dynamic in history and removing those contexts, caricaturing Fitzroy to fit a simpler narrative, and declaring, in the words of Booker "You're both the same" when its anything but.
