Well. They aren't exactly "true bretons" no, but what defines that? So your telling me if someone took your home from you, and forced you into exile, or false imprisionment.... you wouldn't be pissed?
The Reachmen and Bretons are the same race but have a different culture. Over 5000 years ago, when elves still ruled Tamriel, the Bretons were servants to the elves, and the Reachmen were free in remote regions the Falmer didn't care about. Then came the Nords and kicked elven butt. Thoroughly.
For the last 5000 years, the Reachmen and the Nords lived in peace, while a faction of Reachmen continued to live in the ways of their distant ancestors in mountainous regions, far away from civilisation. In the Empire-Dominion war, when everyone was distracted, those people seized Markath and ruled it for two years. Then came Ulfric and kicked Witchmen butt. Thoroughly.
The Survivors of the Markath occupants rallied the other Witchmen tribes and called themselves the Forsworn, and started a guerilla war against everyone who isn't a Forsworn.