When the search engine pulls so much more than just a link, there is no need to actually go to the site. ... I don’t have a solution.

Luckily you don't need one. Facebook came up with the solution a long time ago – one that all the major media sites adopted. It's called OpenGraph. It lets the publishers decide exactly how they want to present their content on these sites. Give too much information and the users won't click? Change what information you specify. It all happens on the publisher's side, so they are in full control.