Someone fully understanding a concept ought to be able to use that understanding as a guide to understand analogous unfamiliar topics.

I agree about this normatively – that we ideally should be able to apply the same principle across multiple contexts – but you shouldn't expect it. Whether or not you fully buy the "massive modularity" hypothesis, cognition is very context-dependent. As Mercurial notes, cross-contextual learning is the big thing in education and goes by the name of transfer. They've been working on it for a long time and I think is one of the central issues in practical rationality. If you are primed to think a certain bit of knowledge is cross-applicable, it's not that hard. The real difficulty is spontaneously realizing what is going on, along the lines of the 5-second skills Eliezer recently touched on.