Equivalent quasi-transversal conjecture for Latin squares

Let $L$ be a Latin square. A quasi-transversal is a set of entries containing exactly one entry from each row and each column, with exactly one symbol repeated twice and every other symbol occurring once.

Quasi-transversal conjecture. Every Latin square has a quasi-transversal.

The source states that this is equivalent to the near-transversal conjecture by the preceding observation: deleting the repeated symbol from a quasi-transversal gives a near-transversal, and completing a near-transversal in the prescribed way gives a quasi-transversal. The source gives no resolution status.