But that was the point the OP was making. Not that you couldn’t differentiate between white balance correction and generative fill, but rather that the intent of the change matters for determining if an image is “fake”.

For example, I took a picture of my dog at the dog park the other day. I didn’t notice when framing the picture but on review at home, right smack in the middle of the lower 3rd of the photo and conveniently positioned to have your eyes led there by my dog’s pose and snout direction, was a giant, old, crusty turd. Once you noticed it, it was very hard to not see it anymore. So I broke out the photo editing tools and used some auto retouching tool to remove the turd. And lucky for me since the ground was mulch, the tool did a fantastic job of blending it out, and if I didn’t tell you it had been retouched, you wouldn’t know.

Is that a fake image? The subject of the photo was my dog. The purpose of the photo was to capture my dog doing something entertaining. When I was watching the scene with my own human eyes I didn’t see the turd. Nor was capturing the turd in the photo intended or essential to capturing what I wanted to capture. But I did use some generative tool (algorithmic or AI I couldn’t say) to convincingly replace the turd with more mulch. So does doing that make the image fake? I would argue no. If you ask me what the photo is, I say it’s a photo of my dog. The edit does not change my dog, nor change the surrounding to make the dog appear somewhere else or to make the dog appear to be doing something they weren’t doing were you there to witness it yourself. I do not intend the photo to be used as a demonstration of how clean that particular dog park is or was on that day, or even to be a photo representing that dog park at all. My dog happened to be in that locale when they did something I wanted a picture of. So to me that picture is no more fake than any other picture in my library. But a pure “differentiate on the tools” analysis says it is a fake image, content that wasn’t captured by the sensor is now in the image and content that was captured no longer is. Fake image then right?

I think the OP has it right, the intent of your use of the tool (and its effect) matters more than what specific tool you used.