Hit and run while parked at work - my own carrier wants me to pay collision deductible even though I have UM. Is this right?

Trying to get a sanity check before I push back on my adjuster. My car was hit while parked in the employee lot at my office last Tuesday. Whoever did it took off. Side mirror destroyed, rear quarter panel scraped down to bare metal, dent in the door. Estimate from the body shop is $3,800.

I called my insurance to file a claim. I have collision ($500 deductible) and uninsured motorist property damage on my policy. The adjuster is telling me this has to go through collision because we don't know who hit me, so my UMPD coverage doesn't apply because there's no "identifiable uninsured driver." So I'm on the hook for $500 out of pocket.

That doesn't feel right to me. The whole reason I added UMPD was for exactly this kind of scenario - getting hit by someone who took off. Is there a state thing here? I'm in Georgia. Or am I misunderstanding what UMPD covers?

Also, would filing under collision raise my rates more than UMPD would? I've never made a claim in 12 years of driving and I'd like to keep it that way if possible.