The answer is yes, there is such a thing. They are not contradictory.
I'm assuming you refer to the person; the role; the calling.
Of course there have been intellectuals who do not appear to possess superlative analytical skills and convey lucid accounts of same, OR good at problem-solving, OR even possessing an above average IQ. (Covering some of the uses of the word.)
The reason that they are still considered insightful is that several of the intellectuals' primary and important activities simply do not relate directly to intelligence at all, such as politics, art or spiritual discussion. For example, many saw Andy Warhol as an intellectual. If he was, his instincts and perceptions played a much greater role than thinking in this role.
That doesn't mean that a typical intellectual of any of these types doesn't spend a great deal of their time thinking, reflecting, meditating (on matters of life and the times). Reasoning is a primary activity of intelligent thought, but thinking isn't restricted to reasoning.