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.
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.