Well, everybody does propaganda. When they say they don't do propaganda, that's propaganda.
Governments engaged in geopolitical conflicts do it 24x7x365.
One of the things that an adult has to face growing up, is that at least some of the ideas that you hold in your head, have been cooked up in a think-tank or secret government bureau.
EDIT: If you haven't realized this, then change some to a lot.
So then why wouldn't they do a better job, to avoid detection as "propaganda to suggest that your enemies do propaganda"? Seems likely it's propaganda to suggest that your enemies do "propaganda to suggest that your enemies do propaganda"...