Did you ask them for a letter saying that they have no judgment on record for you at all (assuming that's true)? Perhaps for a letter saying that they have no record of any judgment with that number on it?
Because it's the right thing to do?
What about this: if it's on their website, why don't you get screenshots of the search and provide that to Experian? I mean, sure, that could be faked, but Experian might be willing to investigate to see if you're making it up if you provide them with any kind of evidence you can. Does Experian list the court address, or just the address for this woman? If they list the court address, you could send the court a letter asking what you can do to get this off of your report (or what their credit reporting guidelines are), and about any records they have under either your name or that case number. Hopefully, you'll get a letter back saying "we're not reporting that and we don't have a case number that matches" which you can then forward on to Experian. RobertEG or 06 may have some more insight into other options.