It seems there is a difference between publicise and publish, in that to publicise means to make something known (through a speech or declaration), while to publish mean to release it in print (article, book). Since they are talking about a letter, it is most likely that it will be printed, and therefore published.
To make something public is to take something that was intended to be private and releasing it to the public. To publish something is the act of putting something in physical form, typically print (books, newspapers, etc), but also video. Now, publishing is often part of the process of making something public, but they are two different things.