It appears the "right to be Forgotten" rules apparently have no provision for
appeal or to give the supplier of the information the right to decide if it
was a valid request.
Why should there be a provision for appeal? It's the person's data, and Google isn't an organ of the state offering a social service. They're just some private company that collects data indiscriminately, whether true or false, and publishes it for profit. At best there should be strict identity checking to prevent fraud.
Google doesn't publish any of the information it indexes. A real world counterpart would be to expect every librarian to vet every article in very newspaper, magazine, encyclopedia,book or other document they catalogue for fraud. As unreasonable expectation for them as for Google. Google makes no claim to the veracity of their information, beyond trying to keep obvious attempts to game result sour of searches.
The best way to view this is like those car window washers at the red lights. They start washing your windscreen without asking, and then expect payment as if you'd agreed to this. Similarly, Google goes around publishing stuff about everyone without asking, and without quality control, to make money.
First of all, Google is not intruding an property without permission no taking any action to
Not really, they are following an accepted practice since the start of the internet, i.e. searching for specific terms and returning the results. Unlike Kibo and his all seeing grep; they use those sort results based on their algorithms and store information for quicker access. If you don't want them to crawl your site, a simple HTML tag will stop them unlike window washers who you may have to pull a weapon on to convince them to leave your property alone.
A more relevant real world example would be requiring publishers to remove material from their archives so it would be as if they never existed.
It's perfectly natural to be able to tell Google to stop publishing rumours and hearsay, or even true fact that are embarassing.
I would say that is one POV. Independent of wether or not you consider Google to publish information, the challenge is how to decide what is legitimately able to be removed. When is their a demonstrable public interest in the information that outweighs a right to privacy? Should the press be shutout from Google searches because what they publish could be embarrassing, damaging, and possibly wrong? Get a bad review? Take it down. This path, taken to an extreme, means no negative information would be searchable, no matter if it is true or not.
Finally, how do you address cases where a company has no presence in the EU, but is reachable from the EU? Should they comply with removal requests? Should EU based companies with no presence in China remove material the Chinese find offensive, threatening or otherwise want removed?
I am not saying their shouldn't be a mechanism to address a right to privacy but in the absence of clear guidance it can have many unforeseen consequences.