  We show that any determination of the strong coupling $\alpha_s$ from a
process which depends on parton distributions, such as hadronic processes or
deep-inelastic scattering, generally does not lead to a correct result unless
the parton distributions (PDFs) are determined simultaneously along with
$\alpha_s$. We establish the result by first showing an explicit example, and
then arguing that the example is representative of a generic situation which we
explain using models for the shape of equal $\chi^2$ contours in the joint
space of $\alpha_s$ and the PDF parameters.
