I had a cat run out in front of me from no where. Strangely everything seemed to go in slow motion, and somehow my brain told me not to swerve as my alternatives were to hit an oncoming car or drive straight into a stone wall. I had the family in the car as well, so instincts said to hit the anchors as hard as possible but not swerve. I was on a road I drove on every day, so local knowledge may have helped, plus a bit of experience from having been driving for nearly 40 years.
Does show you need to be concentrating at all times, and expect the unexpected.
Yes, Avoiding something needn't involve swerving, more often than not just braking will do the trick, or even doing nothing at all. I've hit 2 cats in my time, one at night and just didn't get the time to react in either case sadly.
Pete