In one of cases we worked on Google suggested "Brand name - very harmful keywords". It was mainly thanks to "tabloid campaign."

We negotiated with the owners of websites and with a small legal help they deleted the pages where were the brand name and the harmful keywords. Then we use Google Webmaster Tools to inform Google about these changes (Webpage removal request tool).

After that the harmful keyword dissapared from suggesting.

Since than we use it successfully again and again. It seems, Google needs pages where are both brand name and problematic keyword(s) highlighted (title, Hn...).