Gravity assisting

Question

I watched Passengers movie yesterday. There was one detail which stroke my eye. Does it really make sense to use gravity assisting for interstellar travel? I'd imagine that the spaceship would have exactly the same kinetic energy after escaping the gravity field of Arcturus as it did before entering it. So it seems that the whole dangerous passage was unnecessary?

I imagine you only use gravity assisting within the solar system to redirect space probes. But can you use it to escape the solar system? I mean, if you use Jupiter to throw yourself out of the solar system, then don't you also need to escape the gravity field of Jupiter? And then, I guess you'd have lost all the kinetic energy you would have gained by approaching Jupiter?

Thanks again for comments. Can you find any other physics mistakes in Passengers? The venting of the reactor seems a bit dubious, but maybe you have to do so for fusion reactors!