No, if you rear-end someone, it is always (legally) your fault.
This is not always the case. I actually was involved in two accidents on the same day:
1) on the way to my parent's I was stopped behind an SUV at a red light. The SUV suddenly backed directly into me - thankfully not hard enough to set of the air bag, but smashing in my driverside headlights, scratching my bumper and denting the hood. The other driver was found to be fully at fault. And I got almost $900 to repair it. Thankfully there were a lot of witnesses.
2) on the same day, to make me feel better, my parents took me out for ice cream - as they pulled into their parking spot the driver in the car next to the spot swung his door opend and it scraped along the side of my parent's vehicle. The other car was found to be at fault.
I'm guessing if the police were there and gave you a ticket you're SOL unless there were other impartial witnesses who saw the old lady slam the breaks for no reason. I've killed a car in an accident that was totally my fault before and it was not rad.