Hello, RJ Horace - I can shed some light on the "unusual group" claiming descent from Thomas Hicks in the Hicks/Hix Surname (Y-DNA) Project at FTDNA. You are correct that without a sound paper trail, the data is not very useful.
My son is the tested individual who descends from Thomas Hicks. This is through his son, Daniel...to the Hickes of Rehoboth, MA...Ephraim Sr., Ephraim Jr., Moses, to Simeon. From Simeon, there is abundant circumstantial evidence of son, Daniel (c. 1780-1832), who died in Arlington, Vermont, as did Simeon. The renowned Hicks researcher, Veldon Hix, corresponded with me and believes there was some co-mingling of households in census records for Daniel and a confirmed son of Simeon.
This Daniel Hicks (son of Simeon) & wife, Sally Z. Tinkham, had a son, Robert Emmett Hicks whose marriage record confirms both parents names. The next generation is Edmund Douglas Hicks (1856-1934) who appears with his family in census records. There is no disputing as the next generation is another Robert Emmett, and then my father-in-law was born. From there, we're pretty confident on up to my son's birth. :-)
Interestingly, the closest Y-DNA match to my son claims descent from a Joseph Hicks who was in Canada. As this family continues research, they now think their Joseph Hicks is a descendant of a Thomas Hicks who was in Rhode Island after immigration, quite different from the tree for our Hickses. The Y-DNA matching level suggests that my son and his match share a common ancestor who lived about 400 years ago, which takes us to the 1600s. Either they share the same immigrant ancestor or those immigrant ancestors likely have the same father, same grandfather, or same great grandfather.
If enough other Hicks descendants with a paper trail were to get good-resolution testing, we would eventually be able to sort them out, and perhaps even confirm a paternal ancestral line for some with no paper trail. Small differences may point to one branch or another. It would be great if other Hickses with researched paternal lines were to get tested in order to begin establishing DNA signatures for the various branches of Hickes.