  There are very strong observed correlations between the specific
star-formation rates (sSFR) of galaxies and their mean surface mass densities,
{\Sigma}, as well as other aspects of their internal structure. These strong
correlations have often been taken to indicate that the internal structure of a
galaxy must play a major physical role, directly or indirectly, in the control
of star-formation. In this paper we show by means of a very simple toy model
that these correlations can arise naturally without any such physical role once
the observed evolution of the size-mass relation for star-forming galaxies is
taken into account. In particular, the model reproduces the sharp threshold in
{\Sigma} between galaxies that are star-forming and those that are quenched,
and the evolution of this threshold with redshift. Similarly, it produces
iso-quenched-fraction contours in the ${f_Q(m,R_e)}$ plane that are almost
exactly parallel to lines of constant {\Sigma} for centrals and shallower for
satellites. It does so without any dependence on quenching on size or {\Sigma},
and without invoking any differences between centrals and satellites, beyond
the different mass-dependences of their quenching laws. The toy-model also
reproduces several other observations, including the sSFR gradients within
galaxies and the appearance of inside-out build-up of passive galaxies.
Finally, it is shown that curvature in the Main Sequence sSFR-mass relation can
produce curvature in the apparent B/T ratios with mass. Our analysis therefore
suggests that many of the strong correlations that are observed between galaxy
structure and sSFR may well be a consequence of things unrelated to quenching
and should not be taken as evidence of the physical processes that drive
quenching.
