As if it wasn't already? The feedback button may tag it a certain way but the AI company certainly isn't going to let that sweet sweet user interaction go to waste just because they didn't rate it.
Are you under the mistaken impression that hitting a 1, 2, or 3 for bad/fine/good is itself sufficient permission to allow Anthropic to train off your chat?
They explicitly ask, after the rating, whether they can look at your chat. You can just say "no" to that, if you believe that they are following the rules they say they are.
Your original statement of "using feedback gives them permission to train" is just plain false.
Truth be told, I never used the feedback function because of the clauses that reference the functionality in connection with training/service improvement.
Using feedback on your sessions makes that session, and presumably all attached data, fair game for training.