I have an update to this blog post >How A Business can Like Another Business on Facebook.
It is possible for a Facebook Business Page to Like another Facebook Business Page! In order to do this you must an Administrator on the Fan Page.
Go to the page you wish for the business to be a Fan of and under the image you will see “Add to My Page’s Favorites”, click this link.
The window will allow you to choose which of the pages you manage you would like to be a Fan of.