As far as I've always understood it - which may be right, wrong, misleading, mis-representative and all those other things that the folk tradition is built on... On the death of Protestant Queen Anne, regiments in the British army were authorised to wear a black cockade or rosette in their headgear. Given that there was a good deal of support for Anne's Catholic brother James, who had been deposed by William and Mary, it looked likely that james would return to the throne, and so his followers adopted a white version of the same badge. They were known as Jacobites, hence all those songs about the white cockade and the 1715, and 1745 and Prince Charlie etc.....

And there was a lot of Jacobite support at the end of the 17th century throughout all Britain, not just in Scotland. The Highland connection is really more to do with the later period when English jacobite support had been greatly reduced.