Yes, I would agree that anyone DM represents would never be on the list of companies that DM/EDIG can bring to court. They could be on the list that Law Firm X/EDIG bring to court.
Then with my conflict of interest interpretation, we'd have Law Firm X/EDIG against DM/Company Y.
In your interpretation, we'd have Law Firm X/EDIG against Law Firm Y/Company Y.