I believe that Isaac should be unattached from the current parents: Daniel Wilcoxson, Sr. and Sarah "Sally" Wilcoxson (Faulconer)
This posting of the forum question the name of the parents and state the parents are unknown. Perhaps William? "By naming his son William Isaac, is it possible that Isaac's father was named William and he named a son after his daddy first (Isaac) and his grandfather (perhaps a William) second?"
The findagrave website: http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=63970891 of Isaac Wilcoxson also state that his parents are Daniel Wilcoxson, Sr. and Sarah "Sally" Wilcoxson (Faulconer), this seems more likely. Here is the source quoted on the website for Issac Wilscoxson. http://archiver.rootsweb.ancestry.com/th/read/SOUTH-CENTRAL-KENTUCK...
I agree with you and I have done what you suggested. Until we get some further sources for both Isaac Wilcox Isaac Wilcox
and
Isaac Wilcoxson Isaac Wilcoxson
We will leave it as is, I have added your sources for Isaac Wilcoxson