That is not entirely true. In the Alelluia antiphon for our Lady of Sorrows, the BVM is said to have won martyrdom even though she did not die.
According to that same link:
“The question arises how the sons of Zebedee, namely, James and John, drank the cup of martyrdom, since Scripture tells that only that James the Apostle was beheaded by Herod, but John died a natural death. But if we read the history of the Church, in which it is told that he also for the sake of his witness (to Christ) was cast into a vessel of boiling oil, and thence went forth as a champion of Christ to receive his crown, and was at once exiled to the island of Patmos, we see that his spirit did not fail at the prospect of martyrdom, and that John did drink the cup of confession that the three children in the fiery furnace also drank, although the persecutor did not shed their blood.” (Commentary on Matthew, book 3, chap. 20)