facts fail.....
Unlike animals, people buy snake oil all of the time ( thousands of tank loads sold every year to say the least.) Take snake oil for baldness for example, people buy it for 2 reasons, they believe it works, they hope it works for them ignoring the facts.
Your post assumes and concludes too much. There is no logical fallacy in Bible faith. Faith is logic based on solid fact like taking medicine that works. The effact should realize after the length of treatment is completed. Those that have faith take the medicine and wait for it to work. Those that do not, don't buy it.
Facts do not trump other facts and that is the sophistry of your argument assuming that faith is based on belief (not a talking horse) and that the basis for faith can be invalidated with any new facts whatsoever.