I vaguely remember hearing some version of this story long ago, during my childhood, probably told by the minister of my home church in St. Louis, MO. I haven't thought of it in years, but today for some reason I did, and I decided to check whether it was true, or failing that, at least find its origin. I'm still not sure, but at least I found the story in an apparently credible history book:

From A History of Kentucky Baptists: From 1769 to 1885 ..., Volume 1 by John H. Spencer and Burrilla B. Spencer (Cincinnati: J. R. Baumes, 1885), page 355-6:

Long Run church is located on the eastern border of Jefferson county, about 18 miles from Louisville, and near a small tributary, of Floyds Fork, from which tributary it derives its name. According to the best authorities, it was constituted in 1797.... In 1804, at a log-rolling in the neighborhood, the question as to whether or not a man would be justifiable in telling a falsehood, under any circumstances, was sprung. This illustration was proposed:

"Suppose a man has five children. The Indians come and kill four of them, the fifth one being hidden near by. The savages then ask the father if he has another child. Would he be justifiable in telling them that he had not?"

The dispute grew warm. Some members of the church engaged in it. It finally got into Long Run church, and split it. The "lying party" moved three or four miles west, and were constituted "Flat Rock church" of seven members, the first Monday in March, 1805.