  At high energies, the cross section of a hard exclusive process at finite
scattering angle falls off as a negative power of the center-of-mass energy
$\sqrt{s}$. If all involved quark-gluon compositions undergo hard momentum
transfers, the scaling of the fall-off is determined by the underlying valence
structures of the initial and final states, known as the constituent counting
rules. It was argued in the literature that the counting rules are a powerful
tool to determine the valence degrees of freedom inside multiquark states when
applied to exclusive production processes. However, we demonstrate that for
hadrons with hidden flavors the naive application of the constituent counting
rules is problematic, since it is not mandatory for all components to
participate the hard scattering at the scale $\sqrt{s}$. The correct scaling
rules can be obtained easily by using effective field theory. A few examples
involving the $Z_c(3900)^\pm$ and $X(3872)$ are discussed.
