?? about accident and vehicle repair

What is the name of your state? WA

I was rear ended on 10/26. I finally got ahold of their adjuster(after playing phone tag for 2 weeks). I had to send him a copy of the police report, since not only has the woman that hit me failed to contact them, her phone is disconnected. I got a call from them today telling me to take it to their adjuster, and that they have an approved auto body shop that I can take it to, have the adjuster look at it, and fix it at the same time-and arrange for my rental car. There is no question as to fault, she rear ended me and the police report shows her at fault.

My question is this- does it make a difference if I take it to a shop of my choice or they pick one for me? I'm just a bit leary because she has the same insurance company as I do so I have no idea who is working for me or against me. I was thinking it wouldn't make much difference where I took it, as long as I get my car fixed, but I've had people tell me that I should chose my own shop instead of theirs.

Thanks!