It could be, however, that the website owner never brought up these arguments. The court does not have to do its own investigation. This is called the “maxim of disposition” in German law. Whatever both parties agree on what is true has be treated as true by the court.
So if the claim that the website itself issued the request to Google servers was uncontested, then this ruling is sound, based on the claims brought forth by the parties in this particular case.
I think it's a slippery slope to imagine/enforce a transfer of agency between the website user and provider, where the latter will try to make the opt-in appear as simple as possible. An ideal opt-in is more than the click of a button, it's an understanding. A button accompanied by a wall of text isn't understanding.