Pay for my repairs off of what the insurance gave me.

My neighbor hit my parked car and broke the taillight and the back paneling. After 1.5 weeks they sent me an appraisal that seems a little low and told me to enter my bank account info, receive the money then take it and the quote to a body shop to get fixed then pay for it with that money. I did that this morning and they guy at the shop asked if I accepted the money and I said no (i havent entered my bank info to their site yet). He didnt say one way or the other if it was good. I gave them the quote and keys and asked if it was going to be more then the appraisal if they would contact me and the insurance company he said he'd go directly to company for payment. My question is, if its more than the initial appraisal can the insurance company say no, and tell me to kick rocks for th extra payment?

I've had this happen twice before and both times the insurance company handled everything with me having no exchange of money.

The insurance company did rent me a car but only after I told them the car was undriveable with a Pic of the tail light hanging off.