I get the point, but it isn't true :)
Newton's laws of Gravity are in fact, incorrect.
They only work on Earth essentially. Well, only with objects and speeds similar to Earth's environment.
If you ask a physicist if he believes in Newton's law of Gravitation he'll most likely tell you "no, because in most cases Newton's laws do not make an accurate prediction." General Relativity is where it's at.
Einstein proved Newton's Laws inaccurate using measurements of Mercury's orbit i believe.
You are correct. Newton believed that gravity was the attraction between objects. Einstein's updated theory shows that mass curves space-time and that curvature is what determines how objects will move.