Google's "anonimized IP" means setting the last octet to 0. At best that is a 256->1 grouping[1]. If you're the only person on your local class C network (x.y.z.0-255), your analytics uniquely map to your IP.

Google doesn't have to lie about how they handle IPs - they document how little anonymity they provide. Anybody claiming GA provides any real anonymity either didn't read the documentation[2] for that feature, or they are lying.

[1] https://news.ycombinator.com/item?id=13639921

[2] https://support.google.com/analytics/answer/2763052?hl=en