I feel this way for a few reasons:
Essentially, he played and played well at the cornerback position much of the season over the opponents slot receiver. He spent much less time in the typical "free" and "strong" safety positions than one might imagine.
Also, Whitner does not have the frame Saban looks for at the safety position. He wants guys who is 6' and above. Yet, Whitner does fit have the critical factors Saban looks for in a corner. Tackling, man to man, ball skills, etc.
Whitner was inconsistent in coverage because they were asking him to play over the slot and still perform his duties as a safety. This led to him peeking into the backfield more than he should. Miami will not ask him to do this. They will allow him to use his outstanding combination of speed, power, agility and acceleration to be a lockdown corner first, and a player in run support second. He has the potential to be just as good if not better at corner.
Lastly, I know this has been chuckled at, but I think Saban would love to move Travis Daniels to Free Safety. This pick would allow him to do that.
Essentially adding two starters for the price of one.