By and by

Coming in this morning, heard a reporter on NPR talking about the reports of medical examinations required by fighter pilots.

That's a misunderstanding of the grammar or a corruption of the longer phrase "required to be taken by."

The preposition makes a difference here. If it was required by fighter pilots, then those pilots were requiring someone else to do it. But in this case, the pilots were required to do it, and so the phrase should be medical examinations required of fighter pilots.