It is hard for me to imagine that this Scripture Annotation is in error. Is there any authoritative Church source that has ever made the same claim as you are making here?
Yes, from the highest authority in the Church, it has been infallibly decreed at the Council of Trent's Seventh Session, on The Sacraments in General, Canon IV.
Trent infallibly decrees that "If any one saith, that the sacraments of the New Law are not necessary unto salvation, but superfluous;.....let him be anathema."
A BOD is not a sacrament, therefore having a desire to be baptized cannot save anyone apart from the sacrament.
And again during the Council of Trent's same session Seven, The Sacraments in General, under heading of Baptism, Trent infallibly decreed in Canon V that "If any one saith, that baptism is optional, that is, not necessary unto salvation; let him be anathema."
That is not all Trent decreed about the necessity of the sacrament of Baptism for salvation, but as long as people choose to ignore the infallible teachings and seek loop holes from other sources, this debate will always amount to those who accept dogma without exception vs all the rest.