Yes. Google does not show most backlinks, but in addition, they could have backlinks via 301's that would not show.
One way to hide links is to send all of the link juice through another website. If you want to boost site A, you built the links you want to hide to site B and then link A from B. For this to be most effective make sure the only outbound link on the homepage of site B is going to site A. Also keep in mind that some of the link juice will be diluted in this pass through and you will lose the link diversity by only receiving one good link. This is something that people often do to hide purchased links from their competitors.
Build links to a domain that is 301'd to your domain. Not a good idea to do that for much of your link portfolio, though.
Get an account on Google.com/webmasters - it should show you backlinks to all your site. If you do Link:abc.com in the Google text box - it will show you only a portion of sites linking to you
adamjthompson has covered it nicely. If you want to hide your links use 301 redirection pages. Google and yahoo don't show all the links anyway (yahoo limits it to first 1000 links).
What is Google's reasoning for not showing all the backlinks? I mean what are they getting out of doing that?
Google is protecting the webmaster by not showing all their backlinks to their competitors. They show you all the backlinks in google webmaster tools (where you have already verified that you own the website).
What do you mean "hidden" backlinks? Hidden from what. They are never really hidden (unless they don't exist and then they aren't backlinks, are they?). Do you mean they don't display in Google Webmaster Tools. Even in Google Webmaster Tools, Google doesn't display every link, even if it has "found" them by indexing the page. Do this experiment. Print out a list of your backlinks from Yahoo Site Manager. Pick one that is not on Google's list. Now come up with a search term that allows you to search Google for the specific page that the backlink appeared on. Does the page show up in Google? If so, the Google has your link and is simply choosing not to show it to you.