Some people do "see" implication and "see" the solution to Wason's card puzzle without learning about Boolean relationships, without any previous encounters with an academic logic course.  It's a skill they've somehow developed in everyday encounters with the real world.

It was in the early 70's, just after Wason had published his book. I was listening, with a colleague, to a boring seminar in which the speaker, a physicist talking about systems theory, was wandering in and out of pseudoscience.  At least that was my opinion and that of my colleague, who was a physicist with very little tolerance of pseudoscience, and one who was getting visibly irritated with the speaker.  I could see he was preparing to launch an attack.

I thought it best he not attack because I knew the guest speaker was highly regarded by many of the attendees; they would be embarassed by the kind of attack I knew would be coming.  I presented the about-to-be attacker with Wason's puzzle.  It was the sort of challenge he enjoyed.  He momentarily forgot the speaker and in a few seconds gave the correct answer.  I have never seen anyone else get it that easily.  (But I didn't get an opportunity to present it to Feynman.)

He thought a bit more, and gave the answer he felt most people would give.  And he was right: it was the most common answer, to turn over the two mentioned cards.  Then, after a few seconds more, he commented that it was essentially a point common to many logical errors that people make, with no idea they are being "illogical." All-some confusion, confusing necessity with sufficiency, and improperly inverting implications, for example.  I was impressed because I hadn't seen so much to that puzzle.  (I was one of those who got it wrong at first, then quickly saw my error.)

Then he vigorously attacked the speaker with unassailable arguments showing why his thesis was nonsense, arguments the speaker obviously failed to understand.  The audience, largely a New Age group of non physicists we would now call post-modernist, were upset by the interruption.

I was impressed by the reality my companion saw in the abstract relationship of Boolean implication.  He saw it.  He could use it.  He could predict how other people would react to encounters with it.  For him, it was of the real world, "out there"—not merely a construct of human minds.   And I recalled how Feynman, in his weekly seminars, had astonished me with the way he saw deep, obscure abstractions as real-world entities and then showed us elegant ways to visualize them: the Feynman diagram does that, with two abstract conservation laws at once!   "Fenyman's Lost Lecture" is a book about Feynman's use of the "hodograph," a visual tool for "seeing" some rather abstract physics.  It was used by Maxwell and Möbius in 19th century teaching but has been ignored by modern textbook writers.
Those who do easily see the solution to Wason's card puzzle can often corrrectly predict how someone else, if it's someone well known to them, will respond to it: "see" it quickly, or miss it at first and then soon solve it, or miss it but eventually "sort of see" it dimly, or never see it and feel it's a lot of ivory-towered nonsense, "just an alternative way of knowing."