I see you scenario and I raise you the automated car's response.
Car sees deer lurking by the road side. Car blasts deer off the roadside to ensure it doesn't stray into the road.
Kidding aside, there is no reason a car couldn't do exactly what you would in such a scenario. As long as it can recognize that there is a large animal near the road (which it is likely to realise before you would), it can slow down, change lanes etc. It is also able to react long before you would. For example, upon noticing that there is a potential hazard in the road, it could preemptively move the brake calipers as close as it can to the disc brakes to minimise the time required to engage. You wouldn't normally want this in a human driven car because you have to use the feeling in your feet to regulate the brake force. An automated car doesn't have that problem.
If it couldn't prevent a collision, it can also prep all other safety systems to ensure that the collision causes as little damage to the occupants as possible e.g. gets the airbags ready to go etc.
Finally, once the collision happens, it can continue to steer the car out of trouble, which can be pretty important if there are other cars around. Many times, once a car is hit, humans lose control. The automated systems in a car, assuming you haven't hit a wall, can continue to operate until the car comes to a safe stop.
There are many ways for an automated car to do much better than human in most scenarios, including scenarios where an accident becomes inevitable. A computer can also choose to crash in the best possible way to reduce damage to yourself.