Google probably doesn't show them to avoid those competition to gain almost the same backlinks.
Want to display the quality of product or service that your customers can expect? Your fan page is the best place to do that. With the ability to upload photos of your products, describe your products or services in detail and communicate directly with your consumer, you are establishing a trusted brand that people can depend and rely on to fill whatever need you seek to fill in their life.
Google in fact only cares about PR4 through 10 backlinks, and all backlinks count up only if their dofollow, if they are no follow they are only good for link popularity and after the panda update link reputation isn't very admired anymore LOL.
Google does NOT show all the backlinks pointing to a website. Google will not show all the backlinks to prevent people from manipulating the search results. If they showed you exactly what backlinks are used to get a site to the top - then their algorithm would be compromised.
Google has never shown all backlinks. That does not mean they are not aware of them. If you are link building you notice your site rising in the rankings before the links show up as links at Google.