It makes this factoid even more hilarious if the propaganda campaign successfully created the misinformation without actually obfuscating the desired information, but it's kind of irrelevant to the question of whether they should have bothered with the attempt.

Propaganda is relatively cheap and doesn't consume a lot of resources more directly useful to the war effort. You have a half dozen guys coming up with ideas and doing the graphic design, some printers, and you can either let civilians or enlisted put up the posters when they don't have anything better to do.

At that level of cost, if any piece of propaganda makes an impact, it probably pays for the entire campaign.