The article mentions:
An appeals process does at least exist. Before a "mitigation measure" is taken, users can request an independent review of the accusation, but not from a judge; it remains unclear who exactly will handle the appeal. To keep everyone from using the system every time, there's a $35 filing fee (which can be waived by the independent reviewer).
But notably absent is any mention of a filing fee copyright holders need to pay to prevent them from abusing the accusation process.