>What recourse does Google offer if false, defamatory information is found in their search results?

Last I checked, Google was a search engine, an index of websites, not a judge of the contents of those websites.

>What would stop an organized cyber crime group from creating websites with false, defamatory information about people and blackmailing them for payment in order to take down the false, defamatory information?

Libel laws, for one. The correct course of action here, if the claim is not true, would be to sue the publisher of the false information for libel, which would be a guaranteed success, as it is provably false.