I agree with boxing. I think what you read might have meant that if you’re planning on taking a picture, waiting a while, then taking more pictures, you might as well leave the camera on because you’ll waste as much or more juice turning it off and on.
If that’s NOT what the article meant, then it’s just wrong. I mean, I know batteries do drain over time when not used, but think about this… if your battery sat for a week without being used, you could turn it on no problem and use it like normal. If your battery sat for a week powered ON, it would use a ton more juice. Even if it does power itself down, they’re usually just in “hibernate” mode, which still uses more energy than “off.”