That’s a very confusing statement. My server logs don’t filter incoming log entries based on user agent, and certainly not on whether you’re using a “private window” or not.
In addition, the goal of a private/incognito session is to be indistinguishable from regular sessions, otherwise websites can easily discriminate against private sessions (which they’re already trying as hard as they could).
Edit: Wow the number of people on this thread claiming websites should be able to opt people out of logging based on whether they’re using a “private window” (which websites should have absolutely no idea about) makes me question if I’m even on Hacker News.
Edit 2: Chrome sends an X-Client-Data header (which in a sense includes an installation ID, but allegedly has limited entropy) to certain Google properties, and rightfully got a lot of flak for it. It does not do so for incognito sessions. And now we have people arguing that Google should de-incognito incognito sessions to their analytics properties. Crazy stuff.