"the very real question of whether the military should be manipulating domestic media.""
You can't be serious. Of course the military should have a media relations group: media relations is all about language and manipulation of the facts. That is normal and reasonable.
Bribing the media, however, is the "real question". This is a question of ethics, and has less to do with the military than it has to do with freedom of the press. When government is bribing the press, free press is put on notice.
Analogies to Fox news cheapen the weight of this discussion. While Fox is a mouth piece for US government, it is not paid to do this, and that is a significant distinction. They operate within the market, and make alot of money as a propaganda outlet. If the market had been fundamentally altered such that only propagandists could be successful, again you'd have a fair comparison.