There are several good reasons and usually no downside.
- Your own company might move faster
- Your own insurance company might very well pay more, even considering your deductible
- The insurance companies settle-up between themselves later, and your insurer should get back any deductible you may have to pay up front
- Your policy requires you to report accidents, so you might as well see what your insurer will do in comparison with the insurance company of the owner at fault