Can Other Party's Insurance Really Come After Me Over a Year Later?

Before I spend money on a lawyer I wanted to try to get advice on this forum. I was in an accident over a year ago and it was deemed my fault. I have a full coverage policy and my insurance paid for the damages to the other car which happened to be a rental car. I was just contacted by an agency representing the car rental company (over a year after the accident) and they say that my insurance company did not pay for all their expenses. They expect me to pay these fees now. Is this legitimate? Isn't this why I pay for a full coverage policy?

Thanks for any helpful feedback!

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