Here, my insurance company would probably have "made me whole", then pursued the business owner and/or driver and gotten
their satisfaction from the milk company's insurance carrier.
I had a woman ram me from behind in a fast-food restaurant drive-thru, and when the woman's insurance company dragged its feet, my insurance guy told me that he (my insurance) would pay, and then go after the woman's insurance company to get their money back if need be. Good customer service! He had a name for this process, but I can't remember what he called it.
In the end, her insurance paid off after two things happened. First, I called our state insurance commissioner's office just to ask how long an insurance company can drag its feet before paying up. That got their curiosity up, even though it turns out that they have three months, and it had not been that long. They asked who the woman's insurance carrier was, even though I told them it hadn't been that long. I was impressed by how eager they seemed to dig into this "case".
Second, I talked to my insurance agent, and he made a conference call with me to the other insurance company. There was nobody there when we called, but he left a message. This was at about 4pm on a Friday.
Saturday morning, about 08:00, Fed Ex showed up with an overnight letter containing a certified check for the full amount of the estimate I had gotten.
I wonder if the OP's insurance company did, indeed, go after the milk business's insurance carrier to recover their costs. If so, then, as with my incident, none of this would go against his insurance rating. I hope that's the case.