Absolutely.
Just because your insurance subrogates a claim for you, they are not let off the hook from providing the insurance that they are contracted to provide.
For instance, if someone hits your car and you choose to have your insurance company subrogate the claim - that is, pay you and then go after the other driver to recover their money - and your damaged car is vandalized while at the tow yard, they still have to settle with you on the vandalism claim.
- Stuart
