To put it as gently as possible, your parish’s staff member appears to be very confused on these matters.
1. Granting a general indult for the Tridentine Mass is within a pope’s disciplinary authority. Canon law states that the pope “has supreme, full, immediate, and universal ordinary power in the Church, and he can always freely exercise this power” (canon 331). This means that the pope is not hamstrung in his disciplinary authority by a Church council. Even if Vatican II
did proscribe the Tridentine Mass and the priest facing
ad orientem (“to the east”), which it
did not, a pope could legislate otherwise.
2. The current discipline of the Church regarding the celebration of the Tridentine Mass is that John Paul II asked in his apostolic letter
Ecclesia Dei, given
motu proprio (which means it has the force of canon law), that bishops offer “a
wide and generous application of the directives already issued some time ago by the Apostolic See for the use of the Roman Missal according to the typical edition of 1962” (ED 6c, emphasis added). This contradicts with your parish staff member’s assertion that the Tridentine only be offered “on very rare occasion
.”
3. I recommend that any time someone makes assertions that sound problematic that you politely ask that person to substantiate those assertions from the relevant documents. In this case, you might ask this person to show you where in the documents of Vatican II that the council prevented the celebration of the Tridentine Mass and forbid a pope to allow it.
Recommended reading:
Spirit of the Liturgy by Joseph Cardinal Ratzinger (Pope Benedict XVI)