Does sound somewhat crackpotish. It would appear that what these fellows are basing their theory on is the need for some explaination of precession other than the Sun and Moon. However, I was allways under the impression that precession is a natural result of gyroscopic forces and occurs ni nearly all rotating objects. Not only would Earth's gyroscopic precession take place without another star, it would take place even without the Sun and Moon, wouldn't it?
Also, I believe the mass extinctions in the Earth's past have been chronologically linked to the Solar system's orbit around the Milky Way. Currently, we are "above" the plane of the gallaxy, but moving down towards it (I think), which means that at the point in our orbit opposite from where we are now, we will be "below" that plane. It also means that, twice in each orbit, we must pass through the most thickly populated part of the gallactic plane. IIRC, the mass extinctions appear to take place at about these times.