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.