At best, it can become intuitive to ask the right skeptical questions when being shown a claim.
I feel like it's closely related to combinatorial thought. To again steal an example from Papert, he often talks about asking children to count the numbers of possible pairs of colors of marbles given to them. With some formal training it's easy to visualize and pare down to the right information, and it's also easy to visualize the process. Given a variety of colored marbles, I imagine you could easily estimate the magnitude of colored pairs possible. Children cannot and must learn to think that way at a certain point.
In the same way, conceptualizing uncertain events in the larger space of things that could happen and becoming familiar with the extents and limitations of the casual models we all use is a way of thinking that takes a great deal of effort (today) to come to have, but feels intuitive once you do have it. I believe that there's nothing inherently impossible about teaching it if the appropriate tools are available.