Regardless, eyewitness testimony is not reliable[0]. Many people have claimed to seen UFO's, Aliens, and crimes that people did not commit.
0. http://www.scientificamerican.com/article/do-the-eyes-have-i...
0. http://www.scientificamerican.com/article/do-the-eyes-have-i...
In this case; however, we're talking events like person X gave a speech and said Y. This is much more likely to have been heard by many people, so the likelihood of it have happened in the way it was relayed is much higher.
The Torah claims a million witnesses for the revelation at Sinai. I don't see anyone rushing off to become Jewish.
It occurs to me that "number of purported eye-witnesses" may not be a good evidentiary standard.