With the availability of new high-statistics and wide-angle measurements for several exclusive non-$\ensuremath{\pi}N$ meson photoproduction channels from Jefferson Lab, we examine the fundamental scaling law of 90\ifmmode^\circ\else\textdegree\fi{} scattering in QCD that was originally derived in the high-energy perturbative limit. The data show scaling to be prominently visible even in the medium-energy domain of 2.5 GeV $\ensuremath{\lesssim}\sqrt{s}\ensuremath{\lesssim}2.84\text{ }\text{ }\mathrm{GeV}$, where $\sqrt{s}$ is the center-of-mass energy. While constituent quark exchange suffices for pseudoscalar mesons, additional gluon exchanges from higher Fock states of the hadronic wave functions appear be needed for vector-meson production. The case of the $\ensuremath{\phi}(1020)$, where two-gluon exchanges are known to dominate, is especially illuminating.