Agree with much of your comment.
Though note that as GP said, on the Wason selection task, people famously do much better when it's framed in a social context. That at least partially undermines your theory that its lack of familiarity with the terminology of formal logic.
Maybe the social version just creates a context where "if x then y" obviously does not include "if not x then not y". Everyone knows people over the drinking age can drink both alcoholic and non-alcoholic drinks, so you obviously don't have to check the person drinking the soft drink to make sure they aren't an adult.
I for the life of me could not solve the <18 example from wikipedia. but the number/color one is super easy