Why did national security adviser robert mcfarlane, admiral john poindexter, and their aides assume they had the power to act on their own when dealing with iranian moderates and nicaraguan rebels?

I believe the answer is: a secret intelligence "finding" signed by the president

Even if there is no fact about the finding, all of them had legal ground to act on their own since the finding is acknowledge by the president.
The signed finding indicates that even if their actions were a mistake, the the president would take the responsibility for their action.