The sense of this Americanism is that the person over the barrel is in the
other person’s powers or at his mercy. In the days before mouth-to-mouth
resuscitation and other modern methods of life-saving, lifeguards placed
drowning victims over a barrel, which was rolled back and forth while the
lifeguard tried to revive them. Victims were certainly in the lifeguard’s
power and the process is probably the origin of the phrase.