To my mind, figuring out how to explicitly articulate the minimal conditions under which some obvious" fact is true is where the discover and understanding come in. It is a very different process than what a student does on problem set, where the statement and all the relevant conditions are laid out and the main job is deriving the stated implication.
Put another way: research has degrees of freedom on both ends -- you can find/create the answer and the question as pairs, rather than being handed the one and being asked to complete the set. This perspective of course doesn't cover all cases -- notably, that of people chasing down famous open problems. But it is a way in which one can develop a rigorous understanding from non"-rigorous reasoning. When one first starts thinking vaguely about a problem there is nothing there about which to be rigorous.