RORY: Jess made sure that he called the ambulance and that I was okay before he even talked to the police and – .
This lets the viewer know why Jess isn’t with Rory at the hospital. He phoned for an ambulance and made sure Rory was safe before he had to talk to the police about his role in the accident, since he was the driver at the time. After that, he could have joined Rory at the hospital, but is probably (rightly) scared of how Lorelai is going to react to the news.
The Annotated Gilmore Girls 