The general understanding is that noone cares if they're ok with that as training a model (even if a competing service) is not among the exclusive rights of cop

The general understanding is that noone cares if they're ok with that as training a model (even if a competing service) is not among the exclusive rights of copyright owners where their permission is required - if you have a legally obtained copy, you can use it as you want (except for the specific explicitly enumerated use cases that copyright law awards exclusively to the copyright holder) no matter if the copyright holder likes it or not.