Just because a definition -technically- exists doesn’t mean it’s actually used very much, or is the main definition the word is used for. “Public discourse” is correct, at least for Standard American English.
edit: I am not arguing that this definition doesn't exist. As a native speaker I'm saying that it is very rarely used, if ever. A correction to "public discourse", a statement that actually -is- used by native speakers with frequency, is perfectly reasonable. Communication isn't about being technically correct in order to win arguments.