All these clown politicians on TV are smarter IRL too. An anecdote without any proof - one of such people (now deceased) has been my (now deceased) relative's student and I get the feeling he was quite smart.
My guess is - there's the real support and there's the aura, and the aura should be reduced to the size of real support in cases where assassinations and other unpleasant stuff might happen. Real support has little to do with public opinion and debates and such.