Maybe the document you referenced should be interpreted as "William Thomas and Peter Arterburn" instead of "William, Thomas, and Peter Arterburn."
In "Virginia Public Claims," a published record of claims for services rendered during the Revolutionary War, "William Thomas" and "William Arterburn" were reimbursed for driving cattle to supply the Continental or Virginia troops, in 1783. "The Arterburn Cousins" book also has a transcription of this record. William Thomas must have been a friend, neighbor, or perhaps even a relative, of Peter and William Arterburn.
Also, check out the Arterburn DNA Project online for some info on the ethnic origin of the Arterburn family: http://www.familytreedna.com/public/Arterburn/
Charles R. Arterburn