You’re absolutely right for most of this. React falls into the
V of the
MVC pattern. More appropriately, I think it falls into a category called MVVM. With certain things like Redux or Firebase, you can handle a lot of the other parts without needing much of a “server”. But it isn’t designed to manipulate the back-end directly.
A very common pattern that I’m seeing is projects that have back-end, front-end, and shared code/logic. Meteor works this way.
A nice benefit to this pattern is that your back-end logic can be called from anywhere. You could be on a team that develops a web, native mobile, and other front-ends that all call the same back-end.
But you might not need all that. To answer your question directly: React can call out to databases (Firebase being the most popular thanks to it’s authentication systems) and APIs, but I wouldn’t try to force it to handle back-end logic directly.