[alt text: two frames from the Lord of the Rings films, with a caption on each frame. The first caption says, "Deer when they hear a branch snap" and the image is Merry and Pippin panicking and running through the woods. The second caption says, "Deer when a 60 mph car is driving straight at them" and the image is a close up on Merry's face, where he is staring directly at the camera with a fearless expression.]
The phrase "fight or flight" is common, but there are other components that get left out for reasons. One of the big ones is "freeze." People do it too. And, probably not coincidentally, are often mocked for not doing anything even though it's an involuntary physiological response.