On that very page a picture description reads "U.S. President Barack Obama and aides Carol Browner, David Axelrod and Jon Favreau working on a speech (...)".
Interesting. Is there a part of the democatic process that guarantees electing extremely smart people?
Being president requires you to manage so many different things; it couldn't be done by someone who wasn't smart.
https://www.youtube.com/watch?v=JvknGT8W5jA
I think Dubya talked down to avoid alienating a voters suspicious of intelligent people.
The combination of both is a very rare skill that correlates well with intelligence. Note that it requires both emotional & analytical intelligence: you need to understand what motivates people, and you also need to understand the numbers & segmentation well enough to make sure that you're empathizing with the right group of people.
CEO, BTW, requires a similar skillset. I used to think that CEO was a do-nothing role that you got through political favors, and maybe in a couple dysfunctional companies that's still the case. But in a functioning, market-leading company, being CEO requires that you first understand many different perspectives, and that you can synthesize those into a course of action that avoids pissing off any one core constituency too much.
If you take the dual roles that a President embodies: that of "managed to out-politician every other politician"; and that of "is believed by the technocrats of their party to be capable of negotiating foreign policy, trade agreements, and military conflicts"—you end up with a fair proxy for that particular 'evolutionary' measure of intelligence.
It would be difficult for an unintelligent person to get that far without screwing up and making a bunch of mistakes.
I'm not sure if you mean to refer to only American Presidents or national Presidents globally, but there can be a wide range of them, as far as I can tell. Unless you've looked and found that leaders of even the most far-flung of nations are as described?