Saw SSPX's youtube posting of "Crisis Series #32 with Fr Robinson".  I didn't waste my time watching the video, but I browsed the comments.  Here is a legitimate explanation of BOD by someone from the SSPX (i.e. the youtube channel owner).
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I say "legitimate" because they are TRYING to explain it, whereas on this site, i've only come across 1 other individual who tried to break it down into digestible theology (most know that if they try to explain it, the theory will unravel).  Well, this person's theory also unravels, but I give them kudos for trying.  I pray that God will enlighten them as to their error.
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Below is the "vortex of confusion" which St Augustine warned us about.  Read at your own risk.  It hurts my brain.
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Baptism of Desire is an act of perfect contrition in one not yet baptized (which includes at least an implicit desire for Baptism).
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Since it is an act of perfect contrition (which implies supernatural Charity) this implies at least SOME explicit supernatural faith. Faith cannot be entirely implicit. Implicit faith in some doctrines can only be present THROUGH EXPLICIT FAITH in other doctrines. Ignorance, vincible or invincible does not save anyone! It is Faith informed by Charity that saves.
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What must be believed explicitly? The theologians and Doctors are not unanimous.
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All agree that the two prime credibles – “God is” and “He rewards those who seek Him” (Heb. 11:6) – must be believed explicitly for an adult to obtain eternal salvation.
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In addition to these two revealed truths, St. Thomas Aquinas, St. Alphonsus Liguori and many others maintain that, after the promulgation of the Gospel, explicit belief in the Incarnation and the Blessed Trinity is also absolutely necessary for salvation. For example, St. Thomas says: “After grace had been revealed, both learned and simple folk are bound to explicit faith in the mysteries of Christ, chiefly as regards those which are observed throughout the Church, and publicly proclaimed, such as the articles which refer to the Incarnation…” (ST, II-II, q. 2, a. 7.) St. Thomas also says: “And consequently, when once grace had been revealed, all were bound to explicit faith in the mystery of the Trinity.” (ST, II-II, q. 2, a. 8.)
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How is this Faith acquired? Through a missionary; through a Protestant leaving behind a bible; through a personal revelation, (e.g. Job did not belong to chosen people; yet his knowledge of Redeemer and Resurrection of body was extremely clear – and this knowledge, it seems, was given to him in visions while asleep, according to Job 33 15-16)
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In any case, supernatural Faith that God is, and rewards the good (so, a GOOD God is!) is held by all to be absolutely necessary to a desire for baptism. Thus, neither atheists, LaVeyans nor Satanists could have a desire for baptism, even implicit.

No, it wasn't Xavier; it was whoever owns the sspx youtube site. 

   I think Xavier's explanation would've been more confusing, if that's possible.

It’s only Modernist “theologians” who concocted Rewarder God theory in the 16th century.

Alfred Loisy is generally credited as the "Father of Modernism". There's no Modernism before Leo XIII. No Modernist theologian in the 16th century. In the 16th century, there is e.g. Erasmus of Rotterdam, famous Humanist, and Martin Luther, famous Protestant. Modernists come up at the end of the 19th century.