no. The topic at hand is distribution of copyrighted material, and you're talking about reproduction and possibly preparation of a derivative work.
At last in the USA, copyright law defines specific things copyright owners have exclusive rights to:
- reproduction - preparation of derivative works - distribution of copies to the public - public performance - public display
The most immediate issue with AI companies is whether they've made infringing reproductions.
The other possibility is the preparation of derivative works: does an AI response count as derivative of something it's consumed?
Sorry I'm not going to do the analysis for you, though. I'm no longer a bright, chipper IP law scholar.