What amazes me when I hear the Santa Fe airport story is how all of those disparate pieces of information coalesced so rapidly to form that conclusion. I imagine it was something like thirty seconds to a minute...but it's a great example of what the unfettered mind is capable of accomplishing.
From reading comments on this article - and others related to intuition - the biggest barrier for a lot of people appears to be not wanting to innately trust one's intuition, but rather feeling the need to empirically prove those "Eureka!" moments with hard data - usually numbers, sometimes information that's more qualitative in nature. As Jason points out above, the root cause for this is likely tied to the Western education system, in which empiricism, providing supporting evidence beyond a feeling, etc., is pounded into students to the point that the intuitive voice within is completely squelched.
When those moments do arrive, I believe it's important to embrace them and recognize that feeling of acknowledging the absolute truth of a matter. As with all activities, being able to do so requires consistent practice. But once you can break through that mental barrier, the sky is the limit.