As explained in a March 21, 2005 report (pdf) by the Congressional Research Service, "publicity or propaganda" is defined by the U.S. Government Accountability Office (GAO) to mean either (1) self-aggrandizement by public officials, (2) purely partisan activity, or (3) "covert propaganda." By covert propaganda, GAO means information which originates from the government but is unattributed and made to appear as though it came from a third party.
These concerns about "covert propaganda" were also the basis for the GAO's strong standard for determining when government-funded video news releases are illegal:
The failure of an agency to identify itself as the source of a prepackaged news story misleads the viewing public by encouraging the viewing audience to believe that the broadcasting news organization developed the information. The prepackaged news stories are purposefully designed to be indistinguishable from news segments broadcast to the public. When the television viewing public does not know that the stories they watched on television news programs about the government were in fact prepared by the government, the stories are, in this sense, no longer purely factual -- the essential fact of attribution is missing.In case anyone disagrees with the GAO on this point, here's what the White House's own Office of Legal Council had to say, in a memorandum written in 2005 following the controversy over the Armstrong Williams scandal (when it was discovered that the Bush administration had actually paid him to publicly endorse its No Child Left Behind Law):
Over the years, GAO has interpreted "publicity or propaganda" restrictions to preclude use of appropriated funds for, among other things, so-called "covert propaganda." ... Consistent with that view, OLC determined in 1988 that a statutory prohibition on using appropriated funds for "publicity or propaganda" precluded undisclosed agency funding of advocacy by third-party groups. We stated that "covert attempts to mold opinion through the undisclosed use of third parties" would run afoul of restrictions on using appropriated funds for "propaganda." (emphasis added)
The key passage here is the phrase, "covert attempts to mold opinion through the undisclosed use of third parties." As the Times report documented in detail, the Pentagon's military analyst program did exactly that.