If the business doesn't want to host the chat server themselves, they can have a 3rd party provider host it (like Matrix.org) without worrying about the 3rd party having access to the messages
Edit: sorry I should have clarified that I was answering your second question. As for the first question, the user still has to trust the business to a certain extent
Edit: sorry I should have clarified that I was answering your second question. As for the first question, the user still has to trust the business to a certain extent