I worked in the insurance business for a long time, so a little advice...
Since there were no injuries, I would first off try to work with the towing company's insurance company. Most of the time they are more than willing to work with you. Generally speaking, when their insured is at fault, they will do a better job at taking care of you than your own insurance company.
In my recent accident, there was a dispute between the 3rd and 4th vehicles. The 3rd vehicle said he was stopped, but the 2nd vehicle and me (1st vehicle) felt two impacts, which leads us to believe vehicle 3 hit vehicle 2 first, and then vehicle 4 came crashing in. Since there was a dispute, I had to go through my own insurance company (or wait months for them to work it out).
Since I went through my own company, I was responsible for my $250 deductible. I will get that back EVENTUALLY when my insurance company is reimbursed, but it could take months. Also, because I needed a rental car, my company pays 80% of my rental car expenses. I had the rental for 16 days (before giving up and buying my CX-7) and it cost me $122 out of pocket. If I had filed the claim against the responsible party's insurance, it would have come out of his liability and been covered 100%.
If all else fails, by all means use your insurance company. That's what they're there for. However, if you can get the towing company's insurance to take care of this, you may be better off in the long run.
Hope this helps... good luck!