It seems to be the same family. Here is the census information for Edman. It coincides with the information your great-grandmother gave you.
The 1900 White County, Tennessee census: Mabe, Edward (May 1876), Mary (Oct 1878), Martha (May 1890), Virgil (Sep 1899), and Bessie (Feb 1900)
The 1910 White County, Tennessee census: Mabe, Edward (33), Mary (32), Martha (19), Virgil (12), Blosie (10)
The 1920 White County, Tennessee census: Maab, Edward (50), Mary (41), Martha (27), Virgil (21), and Maude (4 yrs 2 mos)
The 1930 White County, Tennessee census: Maab, Edward (55), Mary (54), Myrtle (30),Maude (14), and Treva Moon (10, granddaughter).
If you want I can EMAIL you an ancestor report for Edman. It's over 40 pages. Also can I add your family information to my data file? I upload 8 generations of the Descendants of William Mabe book to my familytreemaker site. For sure your great-grandmother and her family will be in the on-line book.
I don't have any infomation on cystic fibrosis running in the Mabe family line. Maybe you can contact other members of Edman's lines. I have a picture of Edman's father, Samuel N. Mabe. Additionally, I have copy of Samuel's Civil War pension records.