Propaganda was/is created for the purpose of manipulating public opinion and their views towards a certain policy, authority, specific action, etc. Offhand, I can't really think of an argument that would claim that something that was created to manipulate, and does so effectively, is NOT a form of manipulation. Maybe I'm missing the point, but:
If P belongs to set M, then P belongs to set M.
Propaganda isn't necessarily a new thing. It was used to convince all Europeans that indigenous people were bloodthirsty savages. In that case, the rumors ironically aided in the War of 1812 to the point where the Shawnee leader Tecumseh was able to surprise Americans with the use of clever war tactics. It was used to encourage men to join in the armies of World War I under the guise that war was a glamorous thing. It was used to turn neighbours against neighbours as suspicions of enemy 'aliens' arose during times of combat.
It's history speaks for itself.
Propagandists do not address the opposite opinion on a subject. Propaganda is laden with emotional appeals ranging from fear and excitement to lust and hope. Propaganda does not approach a subject objectively but attempts to sway public opinion with catch-phrases, patriotic ferver and hive-mind created consensus. Read "Manufacturing Consent" by Noam Chomsky to understand how propaganda is used
Propaganda entails all of the ingredients of manipulation. They both are done in a strategic manner to gain the approval of others. Both are used by the media, and they also can be used for good or bad. I think that the word "propaganda" sounds better in a big business meeting. Instead of saying "How can we manipulate our customers?", they may say "We have brought in a professional propagandist to help our company grow.". I feel that in this situation it's all about the choice in word play.