Know your rights!
Sounds like you were driving along, a third car did something out of the ordinary, and the accord had to swerve to avoid hitting them and in the process slammed into you.
100% not your fault.
They are claiming that it was your fault because if they can get you to admit to it, and have it in the police report, then fault is already determined in their favor for the insurance proceedings. If I blatantly rear-end someone, I'm still going to come out of my car insisting that the entire incident was their fault even though it's plain that it wasn't. Sad, yet a common and effective tactic.
#1 rule of non-serious accidents: NEVER admit fault.
You have the right to settle the matter in a court of law. The insurance company does not have the final say in everything. It is their JOB to place the smallest cost possible on their company.
You need to assure that your medical costs are covered. That should be your #1 priority. The car comes second, as it's far less important than your knee.
As for the car, they're going to try to total it out on you for a very low price. When you're dealing with them the question you always need to ask is, "Where can I find the same car, in the same condition for that price?", because you're not going to be able to. Let them know that you aren't willing to settle for what's unfair.
You are supposed to be compensated as to not inconvenience you. What's broken is supposed to get fixed/replaced, without providing a significant gain to yourself.
Oh, and
Seriously.
I have a 73 that was t-boned in the driver's door that I'm cutting up. I know you're not close, but you can have the front clip if you want it. I'm sure you'll find parts cheap enough from the hybridz family.
Then again, it's a serious repair project that you might not want to take one.