We have tons of deer where I drive. Many live right in the towns I pass through regularly. The fields on the way to my cabin often have too many count. The fact I haven't hit one is amazing but if I followed your advice, I'd have hit a few by now. While your advice has some merit, and I have told my wife and daughters to be prepared to hit one if swerving is not safe, such as if you have to swerve into oncoming traffic, or off a cliff. But I never made the "no swerving" advice categorical since in many cases swerving to avoid hitting a deer is not more dangerous, plus if you train yourself not to swerve and you hit a moose, it's like hitting a brick wall, and you'd wish you'd swerved.
When I watch the video I wonder if AP played a part in allowing the driver to not pay as much attention. Yes, the deer comes up abruptly but it's standing on the road. I don't care how dark and fast I am going, I am looking at the road with enough time to stop if there's something there. The deer that dart out I can understand but this accident looked somewhat preventable to me. Then again, I wasn't there so perhaps I am wrong.