If the transition results strictly from the absorption or emission of a photon, then the allowed transitions must retain the same spin multiplicity.  That is, singlet-singlet and triplet-triplet transitions would be allowed (ΔS = 0) but singlet-triplet or triplet-singlet transitions would be forbidden.  These "forbidden" transitions still occur, though much more slowly, by other, non-radiative means.

Earlier I should have said ΔS = 0 for the allowed transitions.  In a magnetic field, there are 2S + 1 spin energy levels (S = total spin) and allowed spin transitions obey ΔS = ±1, but this is not the case here.

I gather that it is possible for triplet-singlet transitions to occur (as noted in the reference in my previous message) but I do not know about the "reverse the spin of the electrons" problem that your teacher was referring to.  Your teacher may have been thinking about the selection rules, which say that absorption or emission of a photon alone does not affect electron spin.

One problem I see it that, once intersystem crossing from and excited state singlet to excited state triplet occurs, relaxation by "internal conversion" to a lower triplet state (allowed = fast) occurs very rapidly compared to the intersystem crossing rate (forbidden = slow).  Because of this, the molecule would have to go "uphill" in energy to go from the lower excited triplet state back up to a more excited triplet state that is closer to the same energy level as the excited singlet state so that intersystem crossing would be favorable.

Complicated subject!

Steve