There is literally no room between "saying something in public" and "saying something to the whole world". Public means on the cover of the NYTimes and on the public record forever.
So do I understand you do not want these conversations to be read by anyone except you and the recipient? If you don't mind please send the link to a backup of your message I promise I would not read them but I want to make sure you have nothing to hide. Just in case.
No, public literally just means "in a place that isn't private". It doesn't mean that the utterance will be recorded forever verbatim, or that the scope of the non-private place is "the entire world". New York Times may be public, but so is a cafe in a shopping mall. You cannot claim that the two are one or the same, because they are quite obviously markedly different despite fitting the category.
