They do, but when you file a counter notice, you swear on penalty of perjury that you believe the original notice was filed "in error". IANAL either, but it see

They do, but when you file a counter notice, you swear on penalty of perjury that you believe the original notice was filed "in error". IANAL either, but it seems like that means that if you want to take the most expeditious means of getting your content back up, you effectively surrender any recourse to call them on their perjury.