Your statements are accurate insofar as they go.
Soldiers, however, and especially officers, have been allowed to take their personal weapons to war with them, and especially when those weapons were issue-type service rifles that fired standard military ammunition. There's a reasonable chance that the rifle in the Gunbroker auction is a pre-WWI sales rifle and was the personal property of Corporal Conover. In that case, Corporal Conover was entirely within his rights to pass the rifle to his buddy and have the rifle sent home.
For what it's worth.
J.B.