Some members of the Illyrian movement advocated the idea that all South Slavs are Illyrians, that the two peoples share common ancestry. At first, this statement looks absurd (and it could possibly be that it is). Slavic people came to the Balkans only after 6th century. Illyrians lived there thousands of years before. How come they could possibly be connected then? 

Does anybody have some information of how people back then backed this idea? I mean it sounds weird for a large group of people to all follow an idea that is paradoxical of itself. Or it is maybe just that they didn't have as much historical information?