Drilled shafts often have much more cross-section area than is required to support axial loads. I have been taught, and it is also in an FHWA publication, that the one percent reinforcing requirement can be reduced when the cross-section is larger than required to structurally support the axial loads. The text from the FHWA publication FHWA-IF-99-025, "Drilled Shafts: Construction Procedures and Design Methods" (page 362) reads as follows:
"Structural Design Procedure: Minimum Longitudinal Reinforcement
In the case in which there are no moments or shears the minimum steel precentage can be less than the normal structural minimum of one percent. Section 10.9.1 of the ACI Code states that the area of longitudinal reinforcement for concrete columns must not be less than one percent of the gross concrete area Ag. If, however, the cross-section is larger than required by considerations of the structural resistance, then Section 10.8.4 allows a reduced effective area Ag', not less then one half the total area, to be used to determine the minimum reinforcement and design strength. This means that if the column has sufficient axial strength using only half the gross concrete area, Ag/2, then the longitudinal reinforcement ratio can be reduced to 0.5 percent of the gross concrete area, Ag. That is, (rho)min(%)=Ag'/Ag>=0.5 when Ag'/Ag<1, where (rho) refers to percentage of steel. In fact, in many cases in which drilled shafts are designed with large diameters in order to develop enough side and base area to produce adequate geotechnical resistance in soils and in some soft rocks, this criterion can be used."
I realize that the very first sentence of this quote does not agree with your situation of a laterally loaded member. However, the ACI code and commentary does not include this restriction to cases where there are no moments or shears.
Is the diameter of the drilled shaft dictated by the bending structural resistance of the shaft, or to provide the required resistance by the soil? If the diameter of the shaft is dictated by the required soil resistance, then there is extra structural capacity and the above exception applies, in my opinion. If the bending resistance of the shaft controls the diameter, then the situation is more ambiguous.