Family Lore

My grandparents, John Aaron Davis and Lee Ann Brunson, were cousins according to the family.  A number of their descendants and allied family members have sought to track down that family that would connect the two.  Here is a possibility:
<> Lee Ann, d/o Cynthia Rutherford,  was Mary Allis Davis Rutherford's granddaughter.  
<> Cynthia's brother (Lee Ann's uncle), John A Rutherford, married Thursey Pate.  Thus, Alexander Pate, Thursey's father, became Lee Ann's great uncle by marriage.  
<> Alexander Pate was the brother-in-law of Aaron T. Davis (married Thursey's aunt Rachel Pate), and thus John Aaron Davis' great uncle.  
<> The children of John A and Thursey Pate Rutherford would have been Lee Ann Brunson's first cousins and John Aaron Davis' second cousins. 
The family may have assumed that John and Lee Ann were cousins ("the cousin of my cousin is also my cousin") but there were no actual blood ties.