You are only required to have your ID if you are doing an activity that requires it, such as operating a motor vehicle. Police aren't authorized to just ask anyone for their ID nor do people have to carry it if they aren't driving a car or other activity like that.
The question is, does Wisconsin's open carry law require you carry and produce an ID? If no, then they wouldn't have to provide it. If yes, then they would, just like a traffic stop.
The real BS charge is the 'disturbing the peace' charge for all of them, even those who complied. They are being penalized for obeying the law. That is just police looking for revenge from an embarrassing situation that made the news.
They were called to investigate, so they can ask for ID’s of everyone involved. That is legit.
They did not just request identification out of the blue.
However, see:
http://www.freerepublic.com/focus/f-news/2594740/posts