I don't agree. There are a lot of instances where a first year guy instills confidence, discipline (which preserves chemistry and stability), and gets it turned around the first year because the players also feel liberated and play without the added pressure of trying to save a guy's neck. You can still salve a good season, while allowing the new staff to get a head start on their new direction by recruiting.
The bigger problem in staying the course is that you run into a potential lame-duck situation where if by mid-season things aren't going in an acceptable direction recruiting effectively stops, assistants start looking for their next gig instead of game planning, you miss out on scheduling opportunities, etc. That could dig you a hole that all but ensures the next guy needs two years to climb out.
By making a change this offseason, you might have one year of adjustment (year 2) instead of 3, because year 3 your year 1 recruits are already juniors.
I tend to think we're going with the direction of the 2nd scenario anyway, in all likelihood, so we'll get to see that play out.