I would not recommend ignoring the insurance company's claim against you, or denying to them that you were involved. They will not spend the time to deal with you, they will sell the claim to a collection agency, and those goons will start coming after you for the $2500 and then your life will get about 3 times more unpleasant even than it is now.
Also, be honest with yourself, you have to know what's going on in the road far ahead, not just watch the one car in front of you. I'm trying not to be glib and trite and condescending, because I know accidents can happen to anybody, but they do teach you in driver's ed to watch 2 cars in front of you. My point is mainly that you will have a very hard time dodging responsibility for this rear-ending.
Contact the other guy's insurance co. Explain what happened, you don't think you're entirely at fault, and that the repair bill is inflated, and offer them for example $1000. If they don't want to deal, call your insurance co and let them handle it. If and when your rates go up, shop around for a new insurer and compare rates. If you can't find anything better, then at least you get to pay a little more each month rather than coughing up 2 Large all at once on the spot.
As you can probably guess, I had a similar situation, except I was riding my bike so no possibility to get insurance to cover it. Ha ha. I hid behind a lawyer for a while who basically did nothing, after a year or so the collection agency was threatening to ruin my credit so I coughed it up. I wish I'd handled it differently so I'm passing my experience on to you.
Good luck.
