No, they're arguing that baptism of desire is church teaching because of Trent.

Which... I don't think Trent definitively ruled out the anti BOD position since again, it was addressing Protestant errors, but I think Trent clearly *allows* the BOD position.

Nowhere does Trent say it is possible or certain to be justified, let alone saved via contrition or a desire for the sacrament - it in fact teaches justification *cannot* be effected with desire alone. It'd be nice if BODers would stop making the above claim and comprehend what Trent does say......

Speaking of justification and the one sacrament of baptism specifically, Trent says:
[Justification] "since the promulgation of the Gospel, cannot be effected, without the laver of regeneration, or the desire thereof, as it is written; unless a man be born again of water and the Holy Ghost, he cannot enter into the Kingdom of God".

From this we know 3 things for certain:
1) Justification cannot be effected without the sacrament ("laver of regeneration").
2) Justification cannot be effected by desire only for the sacrament.
3) That we must be baptized with water, i.e. born again of water and the Holy Ghost, just "as it is written" in order to obtain justification.

Note that Trent does not even teach that the sacrament itself certainly effects justification because it could be received unworthily, rather, Trent only says that without it, justification is impossible.  

No, they're arguing that baptism of desire is church teaching because of Trent.

Which... I don't think Trent definitively ruled out the anti BOD position since again, it was addressing Protestant errors, but I think Trent clearly *allows* the BOD position.

How can Trent "allow" the opposite of what it's teaching?  Trent teaches baptism is necessary for salvation. So Trent is saying baptism is necessary, but also that baptism is not necessary? 

Yes, this is one of the great mysteries that BODers, who insist that a BOD is a dogma, never acknowledge. This always reminds me of what Fr. Wathen said about something else, but it applies here as well.... "If we must argue away all the other doctrines of the Faith, and deny the reality of the very cosmos, we will hold to this one dogma."

Makes sense. Christ died for teaching EENS.