Give me examples of it being used in this context.
The original Half Life had 50+ developers according to moby games. Valve had trouble getting a publisher for that. I doubt you could find anyone not referring to them as independent developers back then. Ended up published by Sierra back when they were the big dick publisher around.
00's stuff like Double Fine switching publishers left and right. They got games published by Activision I think.
Don't see how that's different from Obsidian.
How about all the games that are published by Devolver Digital these days?
Would you say that Free Lives doesn't count as an independent games studio, because Genital Jousting was published by Devolver Digital?
Do your own googling for articles using the exact wording you want.