While your misunderstanding goes to motive, it's not directly to do with your beliefs about the motives of Bush.
Your conspiracy theory regarding Bush's motives could be used to claim the information was presented as a shill and thus qualifies as propaganda. This is probably where you got the idea (which you fumbled into an improper definition). You need to understand why it qualifies as propaganda under the conspiracy assumption and only under such.
Let's review the definition and highlight where you lost your way:
You see, it's not ~"information presented that influenced ones position on a cause". It's ~"information presented for the purpose of a specific cause".the spreading of ideas, information, or rumor for the purpose of helping or injuring an institution, a cause, or a person
The only way Bush's information about AlQ in post-invasion Iraq was "for the purpose" of war is to presume that it is not an actual reason for his position but merely presented as a shill.
The difference between "in the purpose of" and "for the purpose of" is subtle but, I believe, within your grasp.