Explaining why s and p orbitals do not interact
According to my chem textbook:
"Molecular orbitals obtained from 2px and 2py orbitals are not symmetrical around the bond axis because of the positive lobes above and below the molecular plane."
Your instructor might be pointing out to the bond-symmetry thing in MO formation between pz and s orbitals extrapolated in most chemistry textbooks. 
But orbital overlap is a result of constructive and destructive interference. As s orbitals are spherical, they have infinite possibilities of orbital overlap with other orbital shapes and thus even overlap with d orbitals (as explained by VSEPR: Valence Shell Electron Pair Repulsion Theory in a similar manner). 
Thus s and px and s and py orbitals do overlap; if you take px to be of lower energy than py and pz, s-px overlapping occurs in boranes (formed by boron, which has one electron in 2px orbital, and hydrogen, which has one electron in 1s orbital), that often dimerize. This is also the case with methane, where px, py-s overlapping occurs, assuming that in sp3-hybridized state px, py orbitals in C bond with H 1s orbitals.