The information does not belong to the aggregator OR to the person the information is about. The information belongs to the content creator (who sometimes has a copyright on that information as well).
If that's the case in the US, that's an important distinction between the USA and Europe: Personal information belongs to a person, not to any content creator. So-called content creators are not allowed to publish information about me that I haven't approved. Content aggregators like search engines are not allowed to spread the work further.
An exception is made for "persons of public interest". This usually means politicians or movie stars who earn their money with public engagements. It does not mean publication of any minor breach of the law, or similar information.
And yes, this applies to the physical publication world as well. 100,000s of books have been called back, causing much more lost money than in Internet parlance, because this law hasn't been respected in the first place.
Btw, and it ain't so that Google has problems or outrageous costs associated with fulfilling this court's request. They have the infrastructure already in place, to cope with the link takedown demands of RIAA et.al.