Auto Insurance: My Liability Insurance Pay when Other Driver is Not Insured, but Not when Hit and Run

I was involved in a hit and run. The other driver backed up into me, cracked my bumper and fled the scene (it would cost $1200 to replace).
I have Liability insurance. When I purchased it, the agent told me that in scenarios where the other driver is at fault and has no insurance, I am covered.
Today, I filed the claim for the hit and run, my insurance company says that the damages are not covered because since it is a hit and run, they cannot determine if the other driver has insurance or no insurance?

Is this legally sound? Do I have a case for contesting this?

Thanks for your help.

Auto Insurance: My Liability Insurance Pay when Other Driver is Not Insured, but Not when Hit and Run