Vaccination rates are definitely part of the equation, and I have no doubt that some parents are still avoiding them because of the reasons you cite as well as a now-debunked scare as suggested in the article, but I don't think that it's entirely inappropriate to consider the possibility that some if not a substantial number of third-world immigrants do not get vaccinated because of basic ignorance to the benefits of vaccinations, a religious or cultural impasse or a general fear and distrust of Western medicine, which brings us back to immigration. If you bring in enough third-worlders, you're going to get a certain percentage that are ignorant, fearful or both.
Immigration is definitely an issue as well. One element in immigrant populations is a large number of unvaccinated adults, which produces a greater susceptible group for any infection and vectors of transmission which aren’t found in a group where adults don’t contract the disease.