"Privately circulated" implies something that's only available to a very small group and not widely available. This might be a fair characterization in the case of some very obscure journals, but we might reasonably expect that most of the universities in the world would have subscriptions to journals such as Nature. According to Wolfram Alpha, there are 160 million students in post-secondary education in the world, not including faculty or people at other places that might have an institutional subscription.

Even taking into account the fact that not all of "post-secondary education" includes universities but probably also includes more vocational institutions that likely don't subscribe to scientific journals, we can probably expect the amount of people who have access to reasonably non-niche journals to be in the millions. That doesn't really fit my understanding of "privately circulated".