Here are two very smart people (an economist and legal/economic theorist), discussing the thesis. Gary Becker won the economics Nobel and Richard Posner is perhaps the most distinguished U.S. appeals judge in the country.

Posner:

Here is a puzzle: effectiveness in senior leadership positions in government does not seem to be well correlated with intelligence. Washington was a better President than Jefferson, though less able intellectually. Franklin Roosevelt, Harry Truman, Dwight Eisenhower, and Ronald Reagan were not as bright as Herbert Hoover, Richard Nixon, Jimmy Carter, or Bill Clinton. Lincoln, a brilliant lawyer, is an exception; Theodore Roosevelt perhaps another exception; and doubtless there are others. But overall the correlation between intelligence and effectiveness in the Presidency may actually be negative...

What is required at the top levels of government is not brilliance, but managerial skill, which is a different thing, and includes knowing when to defer to the superior knowledge of a more experienced but less mentally agile subordinate.

Becker:

Economists have been emphasizing in recent years that that while cognitive abilities of individuals certainly raise their education and earnings, many non-cognitive skills are often more significant. These skills include simple factors like finishing one's work on time, to more complicated ones like good judgments in making decision, or effectiveness at using talents of subordinates. Posner argues convincingly that non-cognitive talents may be of greater importance in determining success at top-level government leadership positions than analytical brilliance and other cognitive skills...

The limited role of top analytical skills might explain why voters, as opposed to intellectuals, typically do not weight heavily the "IQ" of presidential candidates in choosing whom to vote for. The modest value of exceptional analytical skills should also imply that presidents would not place major emphasis on these skills when choosing their top cabinet officers and other high level appointees.

Read the whole thing here. (You have to scroll down. Out of ignorance or pride, the brilliant scholars do not provide permalinks.)