On Eisenhower, at least, the estimate is seriously wrong. An anecdote.
The Administration was issuing some statement that they thought might
get a negative response. Eisenhower's press secretary was worried.
Eisenhower told him, "Don't worry, send them to me if they have
questions and I'll dumb it up." Or as Murray Kempthorn noted, any career
army officer who regularly played bridge and didn't go broke couldn't be
very dumb. Eisenhower was exceedingly sharp; his oral idiocy was put on
quite self-consciously. And you really have to have an excellent command
of English to convincingly mime illiteracy.