My bed is blue and I've never been eaten by a bear. So obviously the blue bed keeps it away and bears are afraid of blue. That seems like pretty solid logic.
Not saying they are right, but blaming the anti vaxxers for the measles outbreak doesn't make sense. The disease didn't magically manifest here, somebody brought it back from vacation, visiting as a tourist, jumping the border(legal immigrants are aupposed to vaccinate), or intentionally.
It's always been here hanging around, someone just brought it back into the sickness cycle by not getting vaccinated and so it evolved and began to spread.
http://www.nbcnews.com/storyline/measles-outbreak/think-u-s-has-measles-problem-just-look-europe-n301726
http://wwwnc.cdc.gov/eid/article/19/3/12-1360_article