Catapulting the Propaganda

From the Democratic CNN/YouTube presidential debates:

QUESTION: … would you be willing to meet separately, without precondition, during the first year of your administration, in Washington or anywhere else, with the leaders of Iran, Syria, Venezuela, Cuba and North Korea, in order to bridge the gap that divides our countries?

[HILLARY] CLINTON: Well, I will not promise to meet with the leaders of these countries during my first year. I will promise a very vigorous diplomatic effort because I think it is not that you promise a meeting at that high a level before you know what the intentions are.
I don’t want to be used for propaganda purposes. I don’t want to make a situation even worse.

EDWARDS: Yes, and I think actually Senator Clinton’s right though. Before that meeting takes place, we need to do the work, the diplomacy, to make sure that that meeting’s not going to be used for propaganda purposes, will not be used to just beat down the United States of America in the world community.

The United States has the world’s largest media organizations: broadcast networks, cable networks, movie studios, magazines, and newspapers. And the Democratic candidates are worried about other countries winning some sort of propaganda war? Do they really consider the country so weak that someone else’s propaganda would outweigh facts? Any examples?