LOL, you're right, I don't think this is related to dog food allergies.
The driver is at fault. The whole point of having stop signs is to get drivers to stop and check the intersection before proceeding. A driver may not see a pedestrian at first, or may see one but think the pedestrian won't cross in front of him. It doesn't matter if it's a person who knows how to cross a street (look both ways first) or a small child or a dog.
The dog's owner is also at fault for not keeping the dog on a leash or in a fenced-in yard, but that doesn't excuse the driver.
Now, turn the question: What if the dog runs in front of the car and causes the driver to be injured, whether from swerving to avoid hitting it or from colliding with it? The dog owner is definitely at fault, even if the driver ran the stop sign.
So both the driver and the owner are at fault. The misdeed by either one doesn't negate or excuse the misdeed by the other.
If you're wondering whether the driver should pay for the dog's medical care, probably the auto insurance company would assign a percentage of fault, say 60% the driver's fault and 40% the dog owner's fault, then cover a percentage of the cost. If the dog damaged the car (dented it, for example), the owner might in turn be liable for a percentage of the repair cost.