In states such as those, a group conducting paramilitary training for the purpose of taking over the state and seceding from the United States might be prohibited. A group of U.S. military war veterans training as a "militia" so as to be better prepared against the possibility of a terrorist assault would not be prohibited.
Of course, the question of how to explain the difference to the nice men in the Bradley fighting vehicles could be vexing ...
Yep - that's what I meant about the statutes being vague. To outside observers, training to repel a superior invading force looks an awful lot like training to overthrow the government, and telling the difference gets into whether or not you can prove intent.