So why is the idea so common? Lots of smart people seem to think it happens; it's one of the most common justifications for gen ed requirements in higher education.
My guess is it's caused by self-reflection being applied to others. While learning a new subject, some concept reminds the student of a similar concept in another subject. The student jumps to the conclusion that learning the other subject has helped in learning this one. (This sort of epiphany has personally happened to me.)
There are two major problems with applying these epiphanies to other students. First, it's likely that cognitive maps are more interconnected among intelligent people. In other words, transfer of learning may work for some high IQ individuals but not for the average person or even the average college student. Second, it's entirely possible to be falsely reminded of another subject. Mental substitution is common and, when you relate a concept in one field to a concept in another, you may be making the mistake of replacing a hard question you don't know the answer to with an easy one you do know the answer to.
I'll close off with one of my favorite bits from Surely You're Joking, Mr. Feynman! which shows the great physicist understood the inadequacy of learning transfer well enough to employ it as a practical joke:
I often liked to play tricks on people when I was at MIT. One time, in mechanical drawing class, some joker picked up a French curve. . . and said, "I wonder if the curves on this thing have some special formula?"
I thought for a moment and said, "Sure they do. The curves are very special curves. Lemme show ya," and I picked up my French curve and began to turn it slowly. "The French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal."
All the guys in the class were holding their French curve up at different angles, holding their pencil up to it at the lowest point and laying it along, and discovering that, sure enough, the tangent is horizontal. They were all excited by this "discovery"--even though they had already gone through a certain amount of calculus and had already "learned" that the derivative (tangent) of the minimum (lowest point) of any curve is zero (horizontal). They didn't put two and two together. They didn't even know what they "knew."
I don't know what's the matter with people: they don't learn by understanding; they learn by some other way--by rote, or something.