We provide an analysis of vector meson photoproduction in the channel of the vector meson decaying into a pseudoscalar meson plus a photon, i.e. $V\to P\gamma$. It is shown that non-trivial kinematic correlations arise from the measurement of the $P\gamma$ angular distributions in the overall c.m. system in comparison with those in the vector-meson-rest frame. In terms of the vector meson density matrix elements, the implication of such kinematic correlations in the measurement of polarization observables is discussed. For the $\omega$ meson production, due to its relatively large branching ratios for $\omega\to\pi^0\gamma$, additional events from this channel may enrich the information about the reaction mechanism and improve the statistics of the recent measurement of polarized beam asymmetries by the GRAAL Collaboration. For $\phi\to \eta\gamma$, $\rho\to \pi\gamma$, and $K^*\to K\gamma$, we expect that additional information about the spin structure of the vector meson production vertex can be derived.