I think the key point is that there is a requirement that the facts being deleted have no significant public interest [0]. So, for example, Boris Johnson can't have his name removed from search results because there's a public interest in preserving the historical record (can't delete facts with significant relevance to the public), but you can have revenge porn deleted (the public really could care less, and doesn't at all benefit from, what you look like naked).

[0] http://curia.europa.eu/juris/document/document.jsf?text=&doc...