Troublesome Triangle

I ran into a problem computing a polygon normal using Newell’s method as described in Christer Ericson’s excellent book Real-Time Collision Detection. In this case the polygon happens to a be a triangle that is close to the origin. So I would guess that Newell’s method would yield a great result. However, this is not true. I only get 2 digits of accuracy in single precision.
Here is the triangle: