I wasn't involved in the internal discussion 19 years ago, but definitely remember the feature being considered to be for the purpose you cited. I also remember

I wasn't involved in the internal discussion 19 years ago, but definitely remember the feature being considered to be for the purpose you cited. I also remember telling classmates that you can use it for logging in to two accounts at the same time on the site we were developing to have an easier time demoing it to the teachers, and getting jokes about "gee you're awfully familiar with the private browsing feature", from which I'd say it was (1) news to people that it also worked the other way around (website doesn't recognise you) because it was worth bringing up, and (2) people demonstrated knowing it's for not leaving the browser history full of NSFW content—and buying gifts for your partner or parent, of course