In the example detailed in the article, I would think people would never even get past the headline -- a heat map for crime waves would have variances at the level of neighborhoods in large cities, and otherwise would look similar to a population heat map. The maps clearly show county data just based on the borders, not even getting into the placement of colors (seriously, northern minnesota is a hot spot for crime?), so a cursory level of critical thought applied to the headline should have caused people to reject it.
Encouraging people to just stop and think about the content they consume should be the first step.