From the description you gave it sounds as if your property damage liability policy should cover the damage that was caused when you hit the lady's car parked in the fire lane. I was unable to determine if before you went into your office to call your husband you left a note or found the owner of the vehicle. Normally in a case such as this you should try to find the owner of the vehicle you hit or leave a note with your name and insurance information before leaving the scene to place a phone call, etc.

If the person would have stayed then the police could have been called to take an accident report. Your insurance should still take the person's claim even with a police report though. And depending upon your state's negligence laws it may be determined that the other person was partly at fault for illegally parking in the fire lane. To find out for certain what your insurance company will do with the other party's claim; contact your insurance agent with the information about the accident.