There are two possible readings of this passage.
BoDers interpretation: "I cannot write a letter without a pen or a pencil." Either one suffices.
Non-BoDer interpretation: "There can be no wedding without the bride or the groom." Both are required.
We've spent the last 10-15 pages arguing about which is the correct reading of this passage.
The Catechism of Trent provides the solution to
your interpretive dilemma:
Regarding Infant Baptism"Since infant children
have no other means of salvation except Baptism, we may easily understand how grievously those persons sin who permit them to remain without the grace of the Sacrament longer than necessity may require, particularly at an age so tender as to be exposed to numberless dangers of death."
Regarding Adult Baptism"On adults, however, the Church has not been accustomed to confer the Sacrament of Baptism at once, but has ordained that it be deferred for a certain time. The delay is not attended with the same danger as in the case of infants, which we have already mentioned; should any unforeseen accident make it impossible for adults to be washed in the salutary waters,
their intention and determination to receive Baptism and their repentance for past sins, will avail them to grace and righteousness."
The Church, in its gold standard Catechism, written by the same theologians who wrote the Council of Trent decrees, interpreted the phrase "
aut ejus voto" as you say that the "BoDers" do, namely that "either one suffices" in the case of adults.