As for the notion of their deliberately preparing false information to see who leaks it, how would that work? Leaking by definition is difficult to pinpoint. If they cannot pinpoint who's leaking official letters, they won't have any greater luck with "false" letters.
I've got a family member that works for Apple - they do (or at least have in the past) something along these lines in order to identify leaks, but not quite to this extreme. Basically everyone gets a slightly different version of the product - no major differences, but there might be a slight difference in an icon or in layout, etc - if something gets leaked they're able to tell what the source was based on the identifying differences.
They could easily use a method like this to try to suss out the source of the leaks, but if they did and it became known the leakers could just resort to re-wording things to convey the gist of the letter without giving the content verbatum. The only way for them to find the leak then would be to distribute various false letters to different people/departments and see which ones get out, and then withdraw the letters. That's when the leaks really start to hurt their internal operation - when people start getting jerked around like that it will really hurt morale and their ability to have an effective flow of information.