Actually, the whole legal issue started with a case of mr. Mario Costeja González wanting to remove a google search that returned news that was printed in a newspaper, and after suing the newspaper no corrections were printed and the article wasn't recalled as it was truthful, non-anonymous, etc. The newspaper article is still available in the archives, but Google has been given an order to hide it from people.

It's not a hypothetical issue - the "anonymous online speech" is a red herring as the very first censored link was removing a link to a truthful newspaper article, and the BBC removed links are again censoring undisputed respectable news article history.