Hancock does a great job in his book. He explains well, what we already know. And, there may have been more than one, but the main event was clearly about 12,800 years ago, as the study of the ice sheet dating shows.
Here is a NASA photo of the “comet pieces” on Mars. It is most probably debris from a supernova explosion that passed through our solar system. Some of this debris would have been captured by our sun’s gravity to become a long period comet, or, perhaps we were hit, along with other planets of our solar system by the initial debris wave. But yes, we do cross that comet’s path.
https://www.nasa.gov/mission_pages/msl/multimedia/pia16204.html
Out of Curiosity (heh), where did you get the info that these are pieces of a comet, as the photo captions only call it “Rocknest”, and could be the result of many causes?