While going through molecular orbital theory, my chemistry teacher mentioned that the reason why there is no significant interaction between $\ce {s}$ orbitals on one atom and $\ce {p_x}$ and $\ce {p_y}$ orbitals on another atom is that the $\ce {s}$ orbitals interact with both lobes of the $\ce {p}$ orbitals, having both in phase and anti phase interactions with these $\ce {p}$ orbitals, taking the z axis to be the internuclear axis.
However, I read that orbitals which do not have the right symmetry simply cannot interact, i.e. their overlap integral is necessarily $\ce {0}$. Thus, is the reasoning given by my chemistry teacher actually valid?