I think the last head of Boeing who knew a thing about aircraft was Phil Condit, worked on a range of Boeing developments, had his own aerobatic aircraft, etc. But that was 20 years ago, Since then the board don't know one end of an aircraft (or a flawed development schedule) from the other. "Oh, no, we hire people to do things like that ...".
Phil Condit may have had aircraft background, but he was far and away the worst CEO Boeing ever had. His decisions - along with his hand picked successor Harry Stonecipher - lead directly to the 787 development fiasco (and several other $billion foul ups that most people have forgotten about since the 787 overshadowed them so dramatically).
Phil Condit was a shining example of the "Peter Principle" in action.
BTW, I knew Phil and his wife Geda (or should I say one of his wives - he went through several) - he came out of Propulsion...