Holy crap Larry...
I just had a similar situation. I was plowed into by another car while driving my Lexus. The insurance Co. (Arbella) estimated the costs and I - like you- couldn't believe how low they came in. I also got a check for a ridiculous amount. The insurance Co, pays you, not the body shop and then you pay them. Hold the check until the job is complete.
The car has a flexible cover over the bumper and it looked like it was a simple repair. I knew the car had lots more damage and squawked like mad. The auto body guy told me to bring the car in and let them take care of the deal. He took the cover off and called the appraiser and I got another check that covered a whole lot more than the first check. The job was done to my satisfaction using Lexus parts and not a penny out of pocket.
