I doubt the legality of that will prevent anyone from doing a quick Googling of prospective employee while considering their employment.

I don't have to tell you I'm not hiring you because I Googled your past and did't like it. I can just tell you that you're not a good fit for our company.

It's unlikely she'll be moving to Finland, and full third-party background checks are de rigueur for many jobs in the United States.