Anonymity and pseudonymity are two orthogonal concepts. Google could easily offer pseudonymity without making any sort of offer of anonymity. Arguing against pseudonyms with "We can't guarantee your anonymity" is nothing but a straw man.
I don't think the everyman views them as separate concepts.
People honestly believe that if you're using a pen name, then you're anonymous to those who you haven't told your real name to. Note even the terminology used here "Real Name", as in anything that isn't your government ID name is not actually a name. Pseudonyms in formal language are 'names', but not so in informal language.
