Significance of white in a tartan

[Touchstone]

The author writes that, at a lecture given on the subject, his authority and knowledge was challenged by one of the audience with the statement that white in tartan signifies it was worn at the Battle of Culloden. Why did he not know?

I'm not sure I even understand how that would work. That only folks with white stripes in their tartans were allowed to fight at Culloden? That they added a white stripe after the battle? (And wouldn't that make it a different tartan?)