This is a question that has stumped us before too.
For more information you can check out this link
http://www.gean-ealogy.com/genealogy/getperson.php?personID=... , but basically...
Your g-grandfather appears in the household of his parents Wm & Susan Warren in 1850 & 1860. I am 99.9% sure (after years of debate and moving back and forth) that William was David & Grisilla's child...not John & Ann Shaw's. I primarily concluded this based on census records, deed records, court records and studying other children of William & Susan Warren. It would definitely appear that William was the brother of the John that married Lucinda Hazelwood and was murdered in Lincoln Co., TN. Since, John and his brother Joseph were born in Indiana, and David is the only one that we know of for sure that moved to Indiana, I truly believe he has been placed with the right father. Some have said that John & Ann Shaw moved to IN also, but I have found no evidence of that, and there children's birth locations certainly don't indicate that. I believe that was thought because of the placement at some point of William & John to John & Ann Shaw.
John & Ann Shaw's son William Edmond was born about 1821, which is why there has been some confusion about whether he was the one born in 1819 or the one born in 1821. However, he died in 1854 and could not be the William that was married to Susan Warren, and therefore the father of your g-grandfather.
I should also note that from what I have seen, oral family history from descendants of the William Jean that married Callie Miles is that William was the son of David.
Please feel free to check out our website and let us know if you have any additions/corrections or questions!! It is kind of hard to explain in a post, but we are always willing to untangle all these fun Jeans!!