Here is an article from the Chronicle of Higher Education (.pdf in case you hit the pay wall) about what happens when university PR promotes research findings in a way that exaggerates or completely misrepresents the findings. Several examples of this are included (Smelling farts cures cancer? What?), including empirical study of how health related research is translated into press releases (Sumner et al., 2014). The Sumner et al. piece found, that among other things, that 40% of the press releases studied contained exaggerated advice based upon research findings.
I think that this is an important topic to address as we teach our student not to simply perform statistical analyses, but to be savvy consumers of statistics. This may be a nice reading to couple with the traditional research methods assignment of asking students to find research stories in popular media and compare and contrast the news story with the actual research article.
If you would like more discussion prompts like this one, here is an additional example of PR and researchers not working well together, see this old post that describes what happened when PR overstates research findings (here, the safety of artificial sweeteners), leading to researchers having to publicly correct their own PR departments. Another gem is this blog post, that describes how media (not a PR department) got there hands on data related to personal fitness trackers and totally misrepresented the findings.