Of course the TLM can be celebrated versus populum: that is how it was done at the Papal Altar of St Peter’s Basilica for over a millenium, because the confessio (the tomb of St Peter) is directly in front of the altar, leaving no room for a priest, deacon and subdeacon to stand in front of the altar facing versus apsidem. The Popes were still facing ad Orientem, however, as the basilica was built so that the Holy Father would face east despite the confessio.
The Missal of Paul VI includes rubrics that seem to imply that the priest is facing the same direction as the congregation (i.e. versus aspidem / ad Orientem).
For example, at the Orate Fratres, we find the rubric: “Stans postea in medio altaris, versus ad populum, extendens et iungens manus, dicit.”
At the Pax, the rubric reads: “Sacerdos, ad populum conversus extendens et iungens manus, subdit.”
At the Ecce Agnus Dei: Sacerdos genuflectit, accipit hostiam, eamque aliquantulum elevatam super patenam vel super calicem tenens, versus ad populum, clara voce dicit:
Ecce Agnus Dei, ecce qui tollit peccata mundi.
Beati qui ad cenam Agni vocati sunt.
Et una cum populo semel subdit:
Domine, non sum dignus, ut intres sub tectum meum, sed tantum dic verbo, et sanabitur anima mea.
Et sacerdos, versus ad altare, secreto dicit:
Corpus Christi custodiat me in vitam aeternam.
At the Postcommunion prayer: “…sacerdos, versus ad populum, iunctis manibus, dicit:”
And, at the Dismissal: “Deinde fit dimissio. Sacerdos, versus ad populum, extendens manus, dicit:”
Clearly the rubrics assume – or at the very least, allow for – facing the congregation and facing the altar to mean opposite directions.