That said, the EU's right to be forgotten applies to search engines. Not to anyone else. That's why, as someone posted elsewhere, the BBC is able to publish a list of links that have been blacklisted by Google because of the ruling.
It is trivial to form the moral argument for the opposite argument: say I am a corporation (for instance DOW Chemical) and I have a right of personhood in my country, remove negative articles about me from the internet.
If a judge orders it Google will do it, they dont make a moral argument back to a court order(generally), and at that point you have taken critical information away from the greater public (say, that the corp is poisoning people.)