The most useful lie of the presser was not the claim that Moore wrote the whole inscription, but rather Nelson claiming never to have interacted with Moore after the alleged assault. In fact, she claimed to have quit her job the next morning so that she would not have to see Moore (supposedly a regular at the restaurant – a claim contradicted by actual regulars) ever again.
The lie claiming Moore wrote the date and venue was a completely unforced error. If she'd simply said she added the two lines after she got home that night, everyone would have shrugged and said, "OK, let's test the ink's age."
Also remember that two of the real waitresses stated they never remembered Nelson working for that restaurant.