Will rental insurance claims affect personal insurance?

In the example you provide, chances are high that the claim will not affect your personal auto insurance.

Typically there are three ways that an insurance company would learn about this occurrence:

1. Subrogation: The car rental company seeks to subrogate (or seek reimbursement) from your personal auto insurance. I would rate this as unlikely in your example.
2. MVR: The police were called to the scene and took a report. Even if the police took a report, your insurance company would only know if they were to be prompted to run a Motor Vehicle Report (MVR) on your account.
3. CLUE Report: The claim was to show up on a Comprehensive Loss Underwriting Exchange (CLUE) report. I would be very surprised if car rental companies subscribe to this service. Regardless, as with an MVR, your personal auto company would need to be prompted to run this report before they would learn of the claim.

I think chances are very high that unless this was reported to the police, your insurance company will never know about the claim and therefore this incident will not affect your personal auto insurance.