What if your record is wrong, and they won't fix it? And what value do you get of the screening? What can you find, that really would matter to a hiring decision, other than extreme cases?
It took me months to get it figured out because the people responsible for serving me just ignored me. They refused to believe they made a pretty massive research mistake. We had different middle names and birth dates.
Either way this would be a PITA, but it seems the easiest thing to do would be to just go ahead and show up in court. The judge would have you there for about 2 minutes before smacking down the lawyer for the side that summoned you, and sent you home. No reason to spend months working it all out...