I've looked through a few more family trees that at least have a more plausible conclusion. James McMackin was born in 1747. He was married to Barbara Myers who was born in 1750. The two of them begot James McMackin who was born in 1790 or 1791. This James McMackin had a sister named Barbara McMackin who was born around 1776. It is this Barbara McMackin who married John Pickler and would appear to be my ancestor.
The James McMackin who was born in 1790 or 1791 had a son named David McMackin who is the ancestor of some people on here. This means that the descendants of John Pickler and Barbara McMackin are not also descended from Elizabeth Frick.
What do the rest of you think? Does anyone know of a cemetery in Carroll, TN with this Barbara McMackin (who may have died in 1869 per some family trees) or John Pickler? There are multiple Barbara McMackins as I'm sure you all know.