Kinematical parametrizations for photon-induced reactions are discussed in detail, with special emphasis on photoproduction of vector mesons. It is shown that the fact that the photon is massless introduces additional singularities in the crossing matrix. A method for extracting these singularities is discussed. "Conspiring" and "evasive" solutions of the constraint equations, at the thresholds and pseudothresholds, of the process γ+V→N̄N for both natural and unnatural parity-exchange systems are formulated. Kinematic factors obtained from the crossing matrix are compared with those obtained from a field-theoretic perturbative calculation for the exchange of a tensor meson. Examples are given that stress the inherent difficulties in correlating factorization, crossing, and the field-theory approach for one-particle-exchange theories.