You don’t get ads with the premium subscription. Have I misunderstood the intent of this correction?

You don't get ads on YouTube with a premium sub, your activity data (views, for how long, what topics, what times of the year, of the day, so on and so forth) is still collected, and appended to your profile, the same profile that is used by AdSense to show you ads around the rest of the web.

They also own the ad slots everywhere else.