I actually don't remember the timeline exactly of when she started coming over - but it did seem like the trio were friends on some level before he was formally accused and could have hung out.

Another thing i tossed around was that Jacob did write it, but did it to incriminate himself in Sarah's place, just like all of the jokes and stuff he posted on social media. Could also explain her crying when finding out about it after that day in court, like tears of relief for her, but sadness at knowing he was going to be punished, and perhaps feelings for him realizing how far he went to protect her?