The relative anonymity that I refer to is the lack of validation of posting profiles. This isn't on a level of layer 1, 2 or 3 but on how providers don't need any information linked to an ID or at times even emails (for those servers that don't require authentication for posting) You could define any email, name and user agent in the header fields as a posting profile and it would just accept it.
However, this particular aspect that in my eyes, as a whole, was a good thing regarding the system it did provide a strong foundation for the systemic spam problem that was seen across the board in all newsgroups. Accountability could not be maintained and the only thing to stop bad posts from getting through was quickly overwhelmed moderators.
So no, this isn't the same level of anonymity that we would expect from modern solutions but there also wasn't the same guardrails and requirements of identity that has been imposed upon the public like with modern accounts requiring email addresses and phone numbers.
There was a time where accounts didn't require an email. Side note, this is precisely why I like XMPP as a concept. Though I have found little use for it due to the network effect.