I found this information in an old book, but I don't know which Anderson brothers it is referring to.
Thomas L. Wilson (1864)
Sufferings Endured for a Free Government or, A History of the Cruelties and Atrocities of the Rebellion--"Facts stranger than Fiction"
MURDER OF THREE BROTHERS.
In the summer of 1862, three young men, brothers, by the name ef Anderson, not liking the way in which the Union men were treated in their vicinity, left their home, which was in Hawkins county, Tennessee, and attempted to make their way to the Union lines in Kentucky. They had reached Clinch river, about seventy-five miles above Knoxville, Tennessee, when they were surprised and captured by a band of Confederate cavalry, and inhumanly shot without mercy by their captors, who had been sent in pursuit of them. After killing them, they threw their bodies into the river, where, not long after, they were found, only fifteen miles from their desolate and forsaken home. The only reason assigned for this brutal murder was, that they were Union men, and were leaving the country.
The story was attributed to Colonel R. Crawford, of Tennessee, one of the Vice Presidents of the State Convention, held in Nashville in 1863.