I was going to compare this with goodreads, but on that site even simple star ratings show the 'reviewer's' name and photo alongside.
If this new amazon setup is truly anon, I'd expect some downward adjustment to the average ranking, and also it seems to be a whole new area for bad actors to exploit. Obviously Amazon still know who the people leaving these ratings, and I guess if someone tries to leave 10 or 20 per day there's going to be consequences. But maybe they're just rating all their favourite books?
Wonder whether you have to own a copy on Amazon to rate it though? That would make sense.
In my experiment (which was with a DVD, not a book), Amazon would have let me rate even though I bought the DVD elsewhere. So I'd say no, you don't have to own a copy, the same as with reviews.
At least, I think it would have let me rate. As soon as I filled in the start rating, the submit button looked active. Since I intended to leave a review, I didn't actually click it at that point.
Never mind! I should have checked more thoroughly. I just checked using another product. Though the submit button looks active, clicking it without including a review and a title isn't allowed. That means the ratings are coming, just as you indicated, when people review from the Kindle app, not directly on Amazon. Obviously, if they're reading on the Kindle app, the book would probably have come from Amazon.
For the record, though, reviews can be left anonymously (or at least pseudonymously) on Amazon already. When leaving a review, I can edit my customer name to make it whatever I want.