IMO, It’s a much tougher problem (legally) than protecting actors from AI infringement on their likeness. AI services are easier to regulate.. published AI generated content, much more difficult.
The article also mentions efforts by news unions of guilds. This might be a more effective mechanism. If a person/union/guild required members to add a tagline in their content/articles, this would have a similar effect - showing what is and what is not AI content without restricting speech.