Factual error: Jack enters the tournament as a recognized white belt but he is scheduled to face Kim who is ranked as a black belt. Tournaments do not allow match ups between white and black belts; it's forbidden in all styles of martial arts.
Factual error: It says that Jerry is running a judo dojo, but when Jack walks in Jerry is teaching his students to punch - judo doesn't use punches.
Answer: If you noticed, Kim was not sitting with the Black Dragons, so it's safe to assume that she didn't approve of their bullying tactics. She also flashed Jack a smile during the fight, so it's pretty obvious she had no interest in getting involved.