Cars do not run out of oil just because someone different is driving. If it did indeed run out of oil it was probably because either a seal got broken in the accident or because it wasn't topped up properly. You can't really blame whoever was driving when the last of the oil went.
If the oil levels were checked regularly, you should contact the insurer and insist that, while the oil did indeed run out after the accident, the leak was caused by the accident and therefor they are responsible.
At the end of the day though, if you make a big claim, the next premium will also be big. It's often better just to ask the person at fault for a cheque but it's too late for that now.