After reading about 50 long chapters, I really cannot believe Denethor made such grave error in interpreting his own vision.
1) He saw a boat of Elven-make
2) He saw boat by Rauros, (the northernmost reaches of Gondor), not by Osgiliath or any other part of Gondor.
3) How many of Gondor's heirs, where actually sent of to their last journeys on boats when they fall within its bounds?
Elven-make boat and Rauros, clearly pointed that Boromir was not going to die that way when in Gondor. How can Denethor miss those clues? Though he was losing his wits , but he definitely did not appear so witless to make such a fatal error.
Even if Denethor missed it, how can Faramir miss those clues? He is deemed wise, and had knack for questioning everything.
It is very clear that they where inviting Boromir's doom by sending him north, away from Gondor.