Am I fully responsible for paying a towing company $2800 for towing and storage fees?

Question Details:

I was in an accident a month ago and my vehicle was towed away. I later was able to find its location at the towing facility. My insurance advised me to not move the vehicle as yet. Did i mention that I only had liability insurance on the vehicle. Then I later found out that the other party's insurance would be liable. It's been a game back and forth. At this point in time. The bill has gone up to $2800 and counting as the day goes along. At this point. This is very high. I am prepared to pay however, I am being told by several individuals that I am not fulresponsible for paying $2800. Important Notice