> If you're releasing with the help of a publisher you're no longer independent.
Dear diary, I was today years old when I learned that Stardew Valley is not an indie game.
> What does it mean to be an indie game developer?
There's no hard-and-fast rule, but generally speaking it means the devs are not subordinate to the publisher.
There are games for which the publisher contracts a studio, therefore the publisher decides and has the last word, these are not indies.
There are others where the publisher provides funding and / or assistance (e.g. managing distribution channels), but doesn't take much or any active part in the development process. These are generally considered indie games.
There are also games which are entirely self-published. These are also, obviously, indie games.
Super Meat Boy, Shovel Knight, or The Witness are self-published indie games. Fez[0], Stardew, or Bastion are not (published respectively by Trapdoor, Chucklefish, and Warner).
Hell, World of Goo ultimately self-published because they didn't manage to convince a publisher, would that have made them "not indie"?
[0] literally one of the subjects of Indie Game: The Movie