When you argue correctness of a statement with which the interlocutor doesn't originally agree, and use a proof-like strategy for doing so, you don't transfer information about environment either, instead you focus their attention on a sequence of statements already accepted, that surprisingly leads to the originally unexpected conclusion.

When you brainstorm, then the observations you seek are exactly the ideas produced by intuition, so you are not asserting anything about something else, instead you are producing the basic observations. When you voice your opinion, assuming you are trustworthy, you communicate your state of knowledge, and your interlocutor believes that your state of knowledge is indeed as you state it.