Why A Chromosome Browser Is Necessary To Prove Distant Ancestry

My mother's father's fan chart showing the problem lines

I'll outline my problem and why the lack of a chromosome browser prevents me from confirming, or disproving a theory. My brickwall is on the line of a 3rd great-grandmother. I'm using my mother's test, at Ancestry, to try to find her parents, with no documentation other than a couple census records from her children stating she was born in Tennessee. 

My 3rd great-grandmother's name was Sarah or Sally Campbell, she married in Indiana. She died young, and before the 1850 Census, so I don't have any information about her place of birth from a census when she was living. There was only one Campbell neighbor named James Trigg Campbell. There isn't much on him either. I assume they are somehow related? 

Using my mother's DNA test at Ancestry the only Campbell matches that are promising descend from George Lafayette Campbell. My mother has a number of matches from his line. He wouldn't be the father of Sarah Campbell but could be a cousin? Researching his family and possible parents has gotten me nowhere. Not many records were kept in Tennessee in that time period. 

Below is a chart with some of the matches my mother has with descendants of George Lafayette Campbell, and the cMs my mother shares with them

George Lafayette Campbell lived in Greene County, Tennessee. Tennessee is where Sarah's children said she was from. It would seem like I have found the right Campbell family for Sarah Campbell. The problem is my mother has another family line from Greene County, TN. 

Below you see photos of William Wray Forgey, Isis Browning his wife, and Elizabeth Wray his mother. Elizabeth Wray's mother was Sarah Campbell, our brickwall. Isis Browning, Elizabeth Wray's daughter-in-law, also had family from Greene County, Tennessee. Isis Browning's grandfather Nathan was born in Tennessee. His father Roger Browning migrated to Tennessee sometime in the late 1700s, and settled in Greene County, Tennessee. His son Nathan migrated to Jackson County, Indiana. It appears there was a migration pattern from that part of Tennessee to Jackson County, Indiana where most of my grandfather's family lived. 

What is my problem? My problem arose when I discovered one of the George Lafayette Campbell matches also was related to the Browning family. Other matches don't appear to be? The theory that we are related to the matches through Campbell could still be correct. 

Precise segment data would help me build out my segment map. My mother has 3rd cousin matches with Browning descendants. The only way to be sure all of these matches match through Campbell would be to make sure they don't overlap with the Browning matches or any other family line matches. Actually I don't know who Nathan Browning's mother was so we could be related to this family through his mother? Or one of Roger Browning's children could have had a non paternity event? So we may not be related through Campbell at all. The only way to be sure of anything, when it comes to more distant matches, is to have a good chromosome map. You would then be able to clearly see if  theoretical matches overlap with the correct segments.

A chromosome map, built with strong 2nd and 3rd cousin matches, is the best way to confirm a relationship. Above you can see my mother's chromosome map, with many 2nd and 3rd cousin matches. I could even add more segments if AncestryDNA provided this data. Ancestry has the largest database which would make it the best company to build out a chromosome map with. There aren't many records surviving from the early 19th century in many places. To use DNA where records don't survive the best way is to build a good chromosome chart. You can't verify distant relationships based on names alone on a family tree because we don't know if there are NPEs? We don't know if there are other relationships? Therefore, I can't be sure I've found, at AncestryDNA, the correct Campbells.