You can say this, but it's not really true. Courts have sliced away at the "independent creation" aspect until it exists in theory but not in practice.

Courts have limited the degree to which you can leverage pre-existing characters, etc., but if you truly create your own thing without relying on the work of others, incidental similarity will not result in infringement. (Of course, incidental similarity might be evidence that you actually copied, instead of independently creating the work.)

It still has to go to trial to be determined. This is used as a punitive mechanism by prominent rightsholders. See the sad tales of Prenda Law, and Rightshaven. I'm not sure what the official term is in the case of "we assume X, but we'll have a trial to see if X is true", but the presumption is that whatever was copied, so it has to go to court. In combination with the "American Rule", that makes everyone shy away from coming too close to copying. You can lawyerly say what you want, the situation is that theoretically you can invent something yourself that's close or identical to some rightholder's ideas, but basically you're punished for it. SO stay away.

> At least in the context of copyright, independent creation of something is not infringement.

The lines what is really counts as "independent" are deeply blurred.