π-ligands in trigonal prismatic complexes

We recently had a discussion here about the symmetry problems for the often postulated s- and p-mixing with the d-orbitals in complexes to somehow allow a d-d-transition. It was pointed out back then that the s- and p-orbitals of the ligands do not possess the $t_2$ symmetry, which is required to mix with the $t_2g$-orbitals in an octahedral geometry.

I looked for some literature but could not find much. The only answer I came up with was that this was only true for pure σ-ligands, because at least the π*-orbital has the $t_2$ symmetry. That is why only π-type ligands influence the ligand field splitting on the side of the $t_2g$.

I think it was Mingos who wrote in his new book that you can predict this by looking at the dual body of your coordination geometry and only if the dual contains triangular faces it will leave no non-boding orbitals. I will finish that sentence with 'in a pure σ-complex' (I guess this is what he wanted to say).

So the dual body of the triangular prism is the triangular bipyramid. So this should leave no non-boding orbitals. And I also checked the character table for the corresponding point-group, all d-ortbials find a symmetric partner in the s- and p-orbitals of the ligands (if I'm not mistaking). So this leaves me with the question, whether π-donor/acceptor ligands have any influence on the ligand field splitting?

This should not be the case here, so for all ligands it's basically up to the electronegativity in the end?

EDIT: I checked it again and just saw that I jumped one row I think, it seems like the $d_xy$ and $d_yz$ orbitals can only be represented by the π-ligands.