As Chalmers and Jackson write in their canonical paper, 'Conceptual Analysis and Reductive Explanation' (pp.7-8):
When given sufficient information about a hypothetical scenario, subjects are frequently in a position to identify the extension of a given concept, on reflection, under the hypothesis that the scenario in question obtains. Analysis of a concept proceeds at least in part through consideration of a concept’s extension within hypothetical scenarios, and noting regularities that emerge. This sort of analysis can reveal that certain features of the world are highly relevant to determining the extension of a concept, and that other features are irrelevant.
On this account, epistemic intensions are scrutable in the sense that we can determine a priori the extension of S in a given scenario V. If S is a statement, then we can determine whether S is true or false at V. Hence, if D is a canonical description of the scenario V, and the statement S is true at V, then the material conditional 'D -> S' is knowable a priori. And if we knew such a conditional for every possible scenario, then S itself would be knowable a priori.
It's a neat picture, but dependent on some fairly hefty idealizations. We mortals are in no position to learn infinitely many such conditionals, for instance. In her AAP talk, Magdalena Balcerak proposed that we could overcome this by seeing conceptual analysis as involving the sort of inductive reasoning familiar from scientific practice. Having formed the hypothesis (that S is true in all scenarios), one tests this against potential falsifiers (e.g. Gettier cases), which may confirm or lead us to revise our original thesis.
That's fine as far as it goes. But note that we can distinguish at least three stages of idealization here:
1) The agent identifies a genuinely possible scenario V (described canonically by D).
2) The agent assesses the truth of S at V (i.e. whether D implies S).
3) The agent repeats steps 1 & 2 for all scenarios, to determine whether S is epistemically necessary.
Inductive reasoning allows us to de-idealize step 3. But the first two steps still seem well beyond the powers of ordinary agents. (Note that D might contain a full microphysical description of a universe in the language of a completed physics!) So it remains an interesting challenge to complete this de-idealization project.
One problem that arises from our step-2 fallibility concerns the diagnosis of terminological disputes. In the idealized case, we can say that substantive disagreements simply concern the locative question of which scenario is actual. If two people disagree about whether S applies to some specified scenario V, then that simply shows that they have different concepts of S. (Some people -- especially in Eastern cultures -- think that Gettier cases still involve knowledge. That simply suggests that they mean something different by the term 'knowledge' than we do. They use it to pick out different possibilities than we do.) But in real life, the disagreement might instead be simply due to one or other party making a mistake. They might misunderstand the scenario, or draw fallacious inferences about what is true at it, hastily judging that D implies S, when in fact further reflection would disabuse them of this notion.
Let us distinguish metaphysical and epistemic interpretations of this problem. The metaphysical worry is that this leaves us with no fact of the matter as to what people really mean by their terms, and whether disputes are substantive or terminological. But this concern is baseless. We can still appeal to counterfactual facts, about what one would say upon idealization, etc. Even remaining within the actual world, there will be facts about one's drawing a fallacious inference, for instance, which might serve as truthmakers for the claim that one's disagreement (say about the Gettier case) is due to error rather than holding different concepts.
Those facts will typically be out of our reach, however, which brings us to the epistemic worry: how can we tell? Here it may help to bring in Chalmers' diagnostic test for terminological disputes: temporarily cut the contested word out of our shared vocabulary, and see if our disagreement persists when we translate our previous claims into uncontested language. (This won't always be easy, and won't work at all for "bedrock" concepts, e.g. perhaps normativity. But then that may indicate that the disagreement is substantive after all.) For instance, we might distinguish contra-causal "free-will_1" from reasons-responsive "free-will_2", so as to dissolve debates about compatibilism. (Though they might re-emerge in debates about genuine moral reponsibility.)
Step 1 may raise even more interesting issues, about how we can identify coherent possibilities in the first place. Perhaps inductive reasoning can help here once again. After all, a coherent possibility is simply one that cannot be ruled out a priori. So if we engage in some reflection, testing it in ways that might plausibly be expected to rule it out if it were incoherent, then surviving such tests provides us with inductive reason to consider the scenario coherent after all.