Hold on, your argument is that they did this on purpose?
My problem with this is that the logic seems similar to the Protestant "one mediator" argument. If a fine distinction can be used in the latter case, it can be used in the former case as well.
I believe the answer to your question is that there's one baptism, and three different ways of receiving it, or at least, I believe that's the pro BOD answer.
It is my opinion that they did this on purpose, whether due to ignorance or malice I cannot guess, but certainly it's not something in there by accident. This forum alone proves it is a teaching that contradicts Scripture, tradition and infallible dogma.
The prot's logic has it's foundation in "Christ did everything, we only need to accept Him as our Savior to be saved." Whereas we Catholics must be told by the Church what we must do in order to be saved, which the prots wholly, some vehemently, reject. So I do not get the connection you are trying to make.
Being that there is only one baptism, and being that Our Lord specifically made the matter water, and He specifically made the form "I baptize thee in the name of the Father, the Son and the Holy Ghost, and since the recipient must desire to receive that one baptism in this manner, if there were any other possible way to receive that baptism, we do not know of it, as such, any other method would only be speculation.
Also of interest is the fact that the only ones who promote a BOD, are already baptized. You will never hear an unbaptized person promote it - never.