I think most people don't really claim, that complexity is gone when properly abstracted, but claim that you don't have to deal with it every single time. That's the purpose of abstracting something.

Simple example: You are not dealing with the complexity of process management of the OS, every time you start any application. Sometimes you might need to, if you are developing software. Or if your application hangs and you need to kill it via some task manager. Most users however, never deal with that, because it is abstracted "away". That's the whole point. Nevertheless, the actual complex work is always done. Behind the scenes.