Hard-scattered parton probes produced in collisions of large nuclei indicate large partonic energy loss, possibly with collective produced-medium response to the lost energy. We present measurements of π^{0} trigger particles at transverse momenta p{T}{t}=4-12  GeV/c and associated charged hadrons (p{T}{a}=0.5-7  GeV/c) vs relative azimuthal angle Δϕ in Au+Au and p+p collisions at sqrt[s{NN}]=200  GeV. The Au+Au distribution at low p{T}{a}, whose shape has been interpreted as a medium effect, is modified for p{T}{t}<7  GeV/c. At higher p{T}{t}, the data are consistent with unmodified or very weakly modified shapes, even for the lowest measured p{T}{a}, which quantitatively challenges some medium response models. The associated yield of hadrons opposing the trigger particle in Au+Au relative to p+p (I{AA}) is suppressed at high p{T} (I{AA}≈0.35-0.5), but less than for inclusive suppression (R{AA}≈0.2).