Well, we have been seeing many polls that remind me of that, such as this:
The math for me is something like this: if Trump voters are now something like 40% and 48% believe, somehow, that Obama was able to influence the rules of engagement when he was a state Senator, it means that roughly 20% of the American people (probably less) believe this crap.
Over the course of time, I have come to the conclusion that any poll will get roughly 15-20% answering: "Yes, I am ignorant/reality-averse." Yes, it is bad that so many people believe stuff that is so clearly wrong, wrong, wrong. On the other hand, these people always exist no matter what the issue. Do we pander to them? Trump does, but I say we should not. Can we lure them into being reasonable, reasoning, informed people? Um, not so sure. Should we marginalize them as we should marginalize dysfunctional professors (see the link at the top)? Not sure, as marginalizing people deepens alienation and that can lead to violence. But I would not want these folks to be shaping outcomes either.
I have no solution, but just want to note that we should not be surprised when 20% of the polled say stuff that is just very wrong. Appalled? Maybe, but surprised? No.