The confusion is the difference between intelligence and common sense.

It's not confusion between intelligence and various mental or physical skills.

The mechanic may or may not have a high degee of intelligence. Most tests will be reasonably accurate in determining whether he does or not. The questions are not complicated. In fact, the question that he posed to the doctor might be typical of such a test.

"Intelligence" is a measure of the capability to process a given set of facts........quickly.........and determining the correct answer from the facts provided.

In the little anecdote, the doctor could be presumed to have lost a point on the question posed. The mechanic may, or may not have figured out this question. However, it would have been independent of his "book smarts" or lack thereof.