We have measured the bending-induced polarization of Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals with compositions at the relaxor-ferroelectric phase boundary. The crystals display flexocoupling coefficients f > 100 V, an order of magnitude bigger than the theoretical upper limit set by the theories of Kogan and Tagantsev. This enhancement persists in the paraphase up to a temperature T* = 500 ± 25 K that coincides with the onset of anelastic softening in the crystals; above T*, the true (lattice-based) flexocoupling coefficient is measured as f13 ≈ 10 V for both compositions. Cross-correlation between flexoelectric, dielectric, and elastic properties indicates that the enhancement of bending-induced polarization of relaxor ferroelectrics is not caused by intrinsically giant flexoelectricity but by the reorientation of polar nanodomains that are ferroelastically active below T*.