Initially, the offense of careless driving is not as serious as it sounds. It is a 2-point violation in New Jersey and rarely will the Court suspend our driving privilege if you are convicted. You have indicated that you were not careless, but you have not stated specifically how the accident happened other than the fact that you rear-ended the car in front of you. The law requires that you keep your vehicle under control at al times, so you may have an uphill battle if you decide to go forward with a trial. Your best bet is to retain a lawyer, who may be able to positively communicate with the driver of the other vehicle. His primary concern may not be so much whether you get points on your license, but be that you are ultimately determined to be at fault in the accident. If your lawyer can then represent to the prosecutor that the other driver is present in court and does not object, the prosecutor may be willing to downgrade your ticket to a 0-point violation.
NJSA 39:4-97, Careless Driving is a very specificstatute in that the State has to prove beyond a reasonable doubt that you drove in such a careless manner as to likely cause damage to person or property. You are correct that the mere fact that there was an accident with injuries is not necessarily proof of careless driving. Did anyone witness the accident? What were the weather and road conditions? Did you or anyone else make any statements against interest? And did the officer get statements from both parties? Keep in mind that NJ allows a defendant to mark with a civil reservation their guilty plea to a traffic summons, which means such plea cannot later be used against a defendant in a civil proceeding [lawsuit; insurance claim].