Like the DMCA
Who is Google to decide if something is in the public interest? Can you even define what "in the public interest" is, or is it one of the I know it when I see it type things?
They are a company so they only care about what is in the companies interest, if they don't de-list something they could end up with court costs defending that.
If the request comes from Joe Average guy, they can ignore it. From a lawyer, or a corporation? Link is toast. Only in the most black and white cases will they not remove the link.
As I said before this will be just like Youtube and the DMCA. If Youtube get a takedown request your video is toast. Even if it perfectly legal and it's now your problem to get it put back. This is abused on purpose to get rid of stuff people don't like, or in error by automatic systems. I have personally experienced this when one division of a major record label proved me with material to promote a bands appearance and approved the final site, but a different division of the same company had the site taken down with a DMCA request a day later.