Character mistake: Characters refer to the Dallas and the Red October as "ships," but anyone stationed aboard a submarine would know to call it a "boat."
Character mistake: As the helicopter crewman sees the Dallas surfacing, he says something along the lines of, "Sub at three o'clock". The next shot is from inside the helicopter and shows the sub and a part of the starboard landing gear retracting pod. This shot puts the Dallas closer to one o'clock. (01:24:00)
Answer: The trench is too deep to recover anything from the bottom of the trench. They were going to fake destroying the Red October, so they need some way to explain the lack of evidence of its destruction (because the remains were on the bottom of this deep trench).